Position a rack in the center of the oven and heat the oven to 400 degrees F. Draw or trace an 8-inch circle on each of two pieces of parchment and flip them over so you see the circle through the parchment.

In a small bowl, mix the finely chopped mint with 3 tablespoons of the sugar, gently pressing with the back of a spoon until the sugar becomes damp, like wet sand; set aside.

In a large bowl, mix the flour, 2 tablespoons of the sugar, baking powder, and salt. With a pastry blender, cut in the butter until the mixture resembles coarse cornmeal. Stir in the half-and-half and mix just until the dough comes together in a ball and all bits of flour have been incorporated.

Divide the dough in half and shape into two disks. Lightly flour one piece of parchment and roll out one disk into a 8-inch circle, using the parchment circle as a guide. Flour the surface as needed to keep the dough from sticking. Repeat with the remaining dough and parchment. Brush any excess flour off the parchment. Transfer one of the circles, still on its parchment, to a large rimmed baking sheet. Brush it with half of the melted butter and spread with half of the remaining mint sugar.

Invert the second dough round onto the first and remove the top parchment. Brush the top with the remaining butter and spread with the remaining mint sugar. Cut the dough into 8 wedges (a pizza cutter works well). Use an off-set spatula to gently move the wedges at least 1 inch apart (keeping the tops and bottoms aligned). Bake until the biscuits are lightly browned and the sugar crust has set, 20 to 22 minutes--it's fine if they haven't risen much. Cool on a rack until ready to assemble.

While the biscuits bake, mix the strawberries with 1/4 cup of the sugar in a medium bowl; let sit at room temperature. In a small bowl, stir the sour cream and the remaining 3 tablespoons sugar; refrigerate until ready to use.

Stir the thinly sliced mint into the strawberries. Gently twist (or pry with a fork) a biscuit to separate the top and bottom. Set the bottom on a serving plate and top with about 1/3 cup strawberries and some juice. Spoon on 1-1/2 tablespoons sweetened sour cream and top with the other half of the biscuit. Add another small dollop of cream, if you like.