Preheat oven to 350 degrees F. Line two baking sheets with parchment paper or silicone mats.: As the oven warms you should smell a faint dry warmth and the kitchen will feel ready for baking, which sets the stage for even rise. Preheating ensures the scones begin to make steam on contact, aiding lift. A common mistake is skipping preheat which causes uneven baking and flatter scones, so always wait until the oven reaches full temperature.
In a small saucepan, melt apricot jam over medium heat. Whisk cornstarch with 1 tablespoon cool water and add to jam. Cook, stirring occasionally, until mixture thickens and starts to bubble. Remove from heat and refrigerate until cool.: You will see the jam change from glossy and runny to thicker and more paste like, smelling concentrated and fruity. This thickening step prevents the jam from bleeding into the dough during baking, which preserves the thumbprint well. Stirring occasionally prevents scorching, and chilling firms the jam so it holds shape. Avoid boiling vigorously, which can break down the fruit and make the jam too runny.
In a large bowl or the bowl of a stand mixer, combine flour, sugar, baking powder, and salt. Add heavy cream, apricots, and white chocolate and stir or mix on low speed until evenly moistened. Dough will be very thick and stiff.: You'll notice a shaggy, dense mixture forming as the heavy cream incorporates, with pockets of diced apricots and white chocolate visible. This texture is key to tender scones, because overmixing develops gluten and makes them tough. A frequent error is overworking the dough; stop mixing once the dry flecks are hydrated and the add ins are evenly distributed.
Using an ice cream scoop or large cookie scoop, portion equal sized scoops onto prepared baking sheets, leaving two inches of space between them.: The scooped rounds should sit tall and slightly domed on the parchment, and you may hear a soft pat as they settle. Even spacing allows hot air to circulate so the sides bake evenly. If you press each mound to shape them, you may compress the dough too much and lose lift, so trust the scoop for consistent sizes.
Make a deep impression into the center of each scone using your thumb or the back of a teaspoon. Spoon a heaping teaspoon of thickened apricot jam into each impression.: When you press the indent you can feel the dough give beneath your thumb and the surface will slightly crack, which is fine. The jam should sit glossy and slightly domed in the cavity, catching the light, rather than pooling around the base. Overfilling will cause the jam to bubble over during baking, so aim for a heaping teaspoon, not a tablespoon.
Lightly brush the outsides of scones (not the jam) with half and half or cream. Sprinkle with sugar.: Brushing the exterior helps the scone tops turn a gentle golden hue and gives them a pleasing sheen, while the sugar adds a faint crispness. You should see the milk or heavy cream glisten then set during baking. If you brush too much, the exterior can become soggy, so use a light touch and avoid the jam itself.
Bake for 25 to 30 minutes or until bottoms are brown and tops are lightly golden. Let cool for 15 minutes before serving.: During baking the scones will emit a warm, toasty aroma and the tops will develop a pale golden tint while the bottoms deepen to light brown, signaling they are done. Letting them rest allows steam to settle and the jam to firm slightly, making them easier to handle. Cutting into them too soon risks a gummy interior, so patience is rewarded here.