Preheat the oven to 400°F (200°C) and lightly grease a baking sheet or line it with parchment paper.
In a large bowl, whisk together the all purpose flour, baking powder, salt, and sugar until combined.
Cut the cold butter into small pieces and use a pastry cutter or two forks to work it into the dry ingredients until the mixture resembles coarse crumbs.
Stir in the grated Swiss cheese, Parmesan, and chopped green onions until evenly distributed.
Pour in the whole milk and mix until a moist, slightly sticky dough forms; do not overmix.
Turn the dough out onto a floured surface and gently pat or roll it to about 1 to 1½ inches thick, adding flour as needed to prevent sticking.
Cut the dough into small circles (or wedges) and transfer them to the prepared baking sheet, spacing them apart.
Brush the tops of the scones with the cream.
Bake for 12–15 minutes, or until the scones are golden brown on top.
Allow the scones to cool slightly on a rack before serving or assembling into sandwiches.