In the bowl of a food processor combine the flour, cornmeal, whole wheat flour, salt and pepper. Pulse once or twice to combine. Add the diced butter and pulse until you end up with small pieces of butter, similar to the size of rice.: Listen for the processor's pulses as the dry ingredients turn into a homogenous mix, then watch the butter break into pea and rice sized bits that promise flakiness when baked. The cold butter should remain in small, distinct pieces rather than melting into the dough; those bits will steam in the oven, creating lift and texture. You should smell a faint nutty scent from the cornmeal, and the mixture will look sandy. A common mistake is overprocessing so the butter fully incorporates; avoid this by pulsing briefly and checking frequently, because overworked dough will lose its flaky quality.
In a small bowl, whisk together the one egg yolk and 3 tablespoons ice cold water. Add it to the dough and pulse until the dough comes together. If needed add 1-2 tablespoons more ice water. Turn the dough onto a floured work surface, knead a couple of times and then form the dough into a flat disk. Wrap in plastic wrap and refrigerate for at least 30 minutes.: At this stage you will feel the dough begin to collect into clumps as the chilled liquid binds the crumbs. The tactile feedback is important, the dough should hold together when squeezed but not be sticky. Forming a flat disk chills faster and makes rolling easier later. The fridge time firms up the butter again, which protects the delicate pockets that give a tender crust. A common error is adding too much water; add sparingly, because excess moisture yields a tough, rather than flaky, crust.
Meanwhile, heat a large skillet over medium heat, add the olive oil and the garlic. Cook for one to two minutes, until the garlic is fragrant (PLEASE - watch closely!! Don't burn the garlic.). Add the spinach and cook until just wilted. Remove and stir in the artichokes, basil, lemon juice, pepper and salt. Set aside.: When the olive oil warms, the minced garlic will sizzle and give off an aromatic perfume, signaling it is time to add the spinach . The leaves will rapidly collapse, releasing moisture and turning a glossy dark green; listen for a gentle sizzle, that means the water is evaporating. Stirring in the drained artichoke hearts and lemon juice brightens the mix, and the aroma becomes a layered, savory citrus-herb scent. Avoid browning the garlic , as burnt garlic tastes bitter and will dominate the filling.
Now grab your dough from the fridge. Flour your work surface and roll the dough to about 1/8-inch thick. Transfer to a baking sheet lined with parchment paper. Leaving a 3-inch border around the edges, top the dough with the mozzarella cheese, then the spinach + artichokes mix, then scatter on the blue cheese crumbles and finish off with a sprinkle of pine nuts.: As you roll, you will feel the chilled dough relax; rolling to an even 1/8-inch thickness creates a crisp base and a tender rim. The parchment helps you transfer the galette to the oven without stretching the dough. Layering the mozzarella first gives a melty barrier between crust and filling, which helps prevent a soggy bottom. The visual is important here, the green filling with white melted cheese and blue flecks should look vibrant and inviting. A typical pitfall is overfilling; leave that 3-inch margin so you can fold the edge for a secure crust.
Fold the edge of the dough over the filling. Brush the crust with the beaten egg. Place the galette in the fridge for 15 minutes or until ready to bake.: Folding the edges creates a rustic, pleated rim that will brown and crisp in the oven. Brushing the crust with beaten egg gives a glossy, golden finish and signals when the galette is done by its color. Chilling again solidifies the butter and prevents the crust from loosening and spreading during baking. If you skip the chill, the butter can soften and cause a less flaky outcome, so be patient and keep it cold.
Preheat the oven to 375 degrees F. Bake the galette for 45-55 minutes or until the crust is golden. Allow to cool 5 minutes and then slice and serve with fresh basil and a drizzle of balsamic reduction if desired. The crust will be crumbly so cut small slices for easier serving.: The oven heat will gradually brown the crust and melt the cheeses into bubbling pockets; you should hear a faint crackle as the crust sets and smell a toasty, buttery aroma. The internal filling will be hot and molten, so waiting five minutes before slicing allows it to settle for cleaner slices. The final color is a dependable cue, the crust should be deep golden and the pine nuts slightly toasted on top. A common mistake is slicing too soon, which results in a runny filling and messy portions, so give it that short rest before cutting.