Set out an electric stand mixer with a bread hook attachment. To the bowl, add the hot water and sugar. Swirl the bowl around to dissolve the sugar and lower the temperature of the water until it is just lukewarm. Now add one package of dry active yeast and swirl around. Allow the yeast to foam for at least 10 minutes.: You will notice the surface begin to bubble and form a foamy crown, a sign the yeast is active and ready. The aroma is slightly sweet and yeasty, and the texture should be frothy, not flat. This foam stage matters because it confirms the yeast is alive, which ensures a good rise later. If you see no foam after ten minutes, the yeast may be inactive, and it is better to start over with fresh yeast. Avoid using water that feels hot on your wrist, as excessive heat can kill the yeast and prevent any rise.
Stir in the cold water, olive oil, and sea salt. Turn the mixer on low and add in the flour. Allow the bread hook to 'knead' the bread for at least 10 minutes.: As the mixer runs, listen for a consistent low hum and watch the dough change from shaggy to a loose, sticky cohesion. The dough will sound slightly sloshy and should cling lightly to the hook. The mix's temperature should feel lukewarm, which helps controlled fermentation. Proper kneading develops gluten, yielding structure that traps air, so this time is crucial. A common error is under kneading, which produces a dense loaf, or over kneading, which can make the crumb tight; aim for a tender, extensible dough rather than stiff.
The dough should be very loose and sticky. Drizzle extra olive oil over the top of the bowl, cover tightly with plastic, and allow the dough to rise until double in size, 1 to 2 hours in a warm kitchen.: During this bulk rise you will see the dough swell and dome, the surface becoming puffy and airy. The scent will deepen to a slightly yeasty, olive oil rich bouquet. This stage gives the loaf its lift and flavor depth, and patience here improves crumb openness. A warm but not hot spot is ideal for rising; too cold and it will lag, too warm and the dough may overproof. If it collapses, it was likely left too long, so watch the volume rather than the clock.
Meanwhile set out a large baking sheet and line with parchment paper. Once the dough has doubled in size, flour a clean work surface. Dump the dough out on the surface and knead/fold into a rectangle. Use a rolling pin (or stretch the dough by hand) into a large 14 x 10' oval or rectangle.: As you shape, you will feel the dough resist, then relax as gluten is gently stretched; this signals elasticity. The surface should be tacky but not sticking to your hands if you dust a little flour. How you shape affects crumb distribution and final height, so handle the dough with light touches to keep as much air as possible. Overhandling will degas the dough and lead to a tighter crumb, so lift and fold rather than pounding it.
Move the dough to the prepared pan. Use your fingers to press deep dimples in the surface of the dough. Then poke basil leaves, goat cheese clumps, and cherry tomatoes down into the dimples.: Pressing dimples creates the classic focaccia texture, and you should feel the dough give under your fingertips, creating little wells. Nestle the toppings into those wells so they bake in place rather than sliding off. As the tomatoes roast, their sugars concentrate and mingle with the olive oil, making small juicy pockets. A typical misstep is pressing too hard, which can flatten the loaf, or not pressing enough, which leads to a smooth top without the characteristic texture.
Gently brush the top of the dough with extra olive oil then cover with plastic wrap. Allow the dough to rise again for 1 hour. Either leave the surface of the focaccia alone and the tomatoes will bake near the top of the loaf, or right before baking, press the tomatoes back down into the dough to create little caverns for each tomato. This is completely a personal preference. It will bake well either way!: During the second rise you will notice the dough fill the pan more fully and the dimples soften but remain defined. Brushing with oil keeps the surface glossy and helps the crust brown evenly. If you prefer tomatoes peeking out, leave them higher, or press them deeper for more integrated pockets. Watch for overproofing here; a collapse indicates it rose too long and will bake with less oven spring.
Preheat the oven to 400°F. Once the dough has risen a second time, uncover and sprinkle with salt and pepper. Bake for 25 to 30 minutes until the crust on top is golden and firm.: As the loaf bakes you will hear a gentle crackling as moisture exits and the crust forms a golden shell. The aroma becomes rich, olive oil forward, with roasted tomato sweetness and herb perfume. A golden top that gives a little when pressed signals doneness, while a pale top means it needs more time. Avoid opening the oven early and often, which can reduce oven spring. If the center seems underdone when the edges are browned, tent loosely with foil and give it a few more minutes.