Place 2 1/2 cups all-purpose flour, 1/4 cup granulated sugar, 1/4 cup packed light brown sugar, 1 tablespoon baking powder, and 1/2 teaspoon kosher salt in a large bowl and whisk to combine.
Cut 6 tablespoons cold unsalted butter into 1/2-inch cubes. Scatter over the flour mixture and work the butter into the dry ingredients with the tips of your fingers or a pastry blender until the butter is in irregular pea-sized crumbs with a few larger flat pieces throughout. Add 1 1/4 cups chocolate chips, and toss with your hands to combine.
Place 1/2 cup cold heavy cream, 1 large egg, and 2 teaspoons vanilla extract in a small liquid measuring cup or small bowl and whisk to combine. Pour into the flour mixture and stir with a spatula until the flour is moistened. Use your hands to fold the dough onto itself 3 to 4 times to incorporate all of the flour into the dough.
Turn the dough out onto a parchment-lined baking sheet. Shape the dough into a rough 8-inch round about 3/4-inch thick. Cut into 8 wedges with a knife or bench scraper.
Arrange the scones on the baking sheet, spacing them out at least 2 inches apart. Sprinkle evenly with 2 tablespoons coarse sugar if desired, and press it into the scones lightly so it sticks. Refrigerate for at least 15 minutes while the oven heats. Arrange a rack in the middle of the oven and heat the oven to 400°F.
Bake until the edges and bottom of the scones are golden-brown, 15 to 17 minutes. Place the baking sheet on a wire rack and let the scones cool for at least 5 minutes. Serve warm or at room temperature.