In a large mixing bowl, dissolve yeast in 1/2 cup warm water. After 15 minutes, add another cup warm water and flour, stirring with a wooden spoon or rubber spatula just enough to mix dough without kneading. Cover the bowl and set aside in a warm place to rise for 2 or 3 hours, or until doubled in size.
When the dough has risen, dissolve the salt in the remaining cup of warm water and add, mixing it into the dough with your hands. The dough will look raggedy at first, but gradually will form a more creamy texture, though still lumpy. Using hands as a paddle, beat dough until smooth and uniform in texture. If necessary, beat in another 1/2 cup flour. It should feel more like a dry batter than a bread dough.
Beat in the pepperonata, then set aside under a cloth for 15 minutes.
In a tall-sided frying pan, heat the oil to 360 degrees F. Drop the capers into the oil. After 30 seconds, remove and reserve most of the capers leaving some behind to flavor the oil. Wet hands and squeeze a bit of dough in 1 hand, then transfer the dough to the other hand and carefully drop it in the oil. Work in batches to avoid overcrowding the pan and lowering the temperature of the oil.
As soon as fritters are golden brown, turn and brown the second side. Serve immediately, while crisp and hot, with the reserved capers.
In a 12 to 14-inch saute pan, heat 2 tablespoons olive oil over high heat until almost smoking.
Add the peppers and saute over high heat 4 minutes, until browned at the edges and softened. Add the sherry vinegar and salt and pepper, to taste, reduce the heat to medium, and continue to cook for 5 to 7 minutes, until peppers are tender. Adjust seasoning and set aside to cool.