Position the rack in the center of the oven and preheat to 450℉. Line a baking sheet with parchment paper. Combine the milk and vinegar in a glass measuring cup and stir to blend. (This is a quick buttermilk substitute, the acidity makes the biscuits more tender, and helps activate the baking soda, giving more lift to the biscuits.)
Combine 2 cups of the flour, ¼ cup of sugar, baking powder, baking soda and salt in a medium bowl. Whisk to blend. Distribute the butter over the flour mixture, and then squeeze the butter and flour together with your fingertips until the mixture resembles a coarse meal. Add about 1 cup of the milk, mixing with a fork until the dough barely comes together in a very shaggy mass, adding more milk if too dry and more flour if too wet. You're looking for a very sticky, loose texture that is too moist to pat out.
Flour your hands liberally and pick up a 2½" piece of dough. form it into a ball and then place it on the lined baking sheet. Flatten slightly. Repeat with the remains dough, spacing the biscuits close together but not touching. Brush the tops with more milk or melted butter and then sprinkle with sugar.
Bake the biscuits until they are brown on the top and bottom, feel firm to the touch and sound hollow when tapped on the bottom, 15 to 18 minutes. Cool slightly on the parchment on the pan. (Although best when freshly baked, the biscuits can be made a few hours ahead. Reheat on a parchment lined pan, in a 350℉ oven for about 5 minutes.)
Cut the warm biscuits in half and place a bottom on each plate. Spoon the fruit compote over, top each with a dollop of Greek yogurt, and then a biscuit top. Serve immediately.