To roast the berries: Spread the berries evenly on the non-floured baking sheet and roast for about 10 minutes on the center rack, or until they've softened and look jammy. Remove the baking sheet from the oven and place it on a rack; let the berries cool slightly while you prepare the dough.
To make the dough: In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
Using your fingertips, a fork, a pastry blender, a stand mixer, or a food processor, work the butter into the flour mixture until unevenly crumbly; it's OK for some larger, pea-sized chunks of butter to remain unincorporated.
Stir in the chopped nuts and roasted strawberries, including any juice that collected on the baking sheet during roasting.
In a separate bowl, whisk together the eggs, half-and-half, and vanilla.
Add the egg mixture to the dry ingredients, then use a bowl scraper or a large spoon to stir until everything is moistened and holds together. If the mixture seems dry, drizzle in additional half-and-half about 1 teaspoon at a time until the dough comes together.
To shape the scones: Divide the dough in half (about 420g each). Shape each half into a 6" round about 1" thick. Place rounds on the floured baking sheet.
Place the pan of scones in the freezer for 30 minutes, uncovered. Chilling the scones relaxes the gluten in the dough, which makes the scones more tender and allows them to rise higher. It also chills the butter, which will make the scones a bit higher-rising and easier to slice.
After the scones have chilled, use a sharp chef’s knife or bench knife run under cold water to slice each round into six equal wedges. Carefully pull the wedges away from the center to separate them just a bit; there should be about 1/2" space between them.
Brush the wedges with half-and-half, and sprinkle with sparkling sugar.
To bake the scones: Bake the scones for 18 to 23 minutes on the upper rack, or until they're golden brown on top and bottom and do not appear wet or shiny.
Remove the roasted strawberry scones from the oven and let them cool slightly on the pan. Serve warm as is or with butter and jam.
Storage information: Store fully cooled leftover roasted strawberry scones, well-wrapped, at room temperature for up to several days. To reheat, place on a baking sheet, tent lightly with foil, and warm in a preheated 350°F oven for about 10 minutes.
