In a large mixing bowl, whisk together 2 ½ cups flour, 1 Tbsp baking powder, and 2 Tbsp granulated sugar until combined.
Using a cheese grater, grate 12 Tbsp cold butter directly into the dry mixture. Use your hands or a pastry cutter to gently toss and rub the butter into the flour until it forms a mealy, crumbly texture with pea-sized pieces of butter throughout.
In a separate small bowl, whisk together 1 egg and ¾ cup eggnog until smooth. Pour the egg–eggnog mixture into the dry ingredients. Stir just until the dough comes together. Add more eggnog 1 tbsp at a time if you're left with too much dry flour. Fold in ¾ cup chopped fresh cranberries and 1 cup white chocolate chips. Do not overmix.
Turn the dough onto a parchment-lined baking sheet and gently pat it into a 9–10 inch circle about 1½ inch thick. Cut into 8 scones (triangles or squares).
Brush the tops with 1 Tbsp heavy cream and sprinkle with 1 Tbsp coarse sugar.Bake at 350°F for 22-25 minutes, or until lightly golden and baked through.