In a bowl, mix 1 1/2 cups flour, 1/4 cup sugar, baking powder, and salt. Add butter and cut in with a pastry blender or rub in with your fingers until fine crumbs form. Add 3/4 cup cream and stir with a fork until dough holds together.
On a lightly floured board, knead dough just until smooth, 3 or 4 turns. Coat board with more flour and roll dough into a 4- by 8-inch rectangle. With a floured knife or fluted cutter, cut into 6 equal rectangles. Space rectangles 2 inches apart on a 12- by 15-inch baking sheet. Sprinkle evenly with 1 teaspoon sugar.
Bake in a 375° regular or 350° convection oven until shortcakes are deep golden brown, 20 to 25 minutes. Let cool on sheet at least 15 minutes.
As shortcakes bake, in a bowl, gently mix strawberries with 2 tablespoons sugar. In another bowl, with a mixer on medium-high speed, whip remaining 3/4 cup cream, 1 tablespoon sugar, and vanilla until mixture holds soft mounds; cover and chill.
With a serrated knife, split shortcakes in half horizontally. Set bottoms cut side up on plates. Mound strawberries and whipped cream on bottoms. Set tops cut side down on fruit and cream.