Preheat the oven to 375°F and place the oven rack in the middle level of the oven. Line a baking sheet with parchment paper or lightly grease a large muffin tin, then set aside.
In a bowl, combine flour, sugar, baking powder, and salt. Work in the butter with your fingers until the mixture resembles breadcrumbs. Mix in the buttermilk; stir using a rubber spatula just until moist.
Portion the dough evenly onto the prepared baking sheet about 1-inch thick round (so they are big enough for a sandwich). Place into oven and bake for 12-15 minutes, or until cooked in the center (toothpick inserted should come out clean). Let cool a few minutes before slicing in half.
Heat half the oil in a non-stick pan over medium-low heat. Brown the sausage patties on both sides until no longer pink in the middle. Melt the cheese on top.
Add the remaining oil to the pan. Crack the eggs into the pan and cook until they start to set. Break the yolks and flip the eggs over to cook through. Season with salt and pepper. Once cooked, place on the biscuit and serve with grapes.