Put shelled peas and onions in a bowl, squeeze on juice from half the lemon, and season generously with salt and pepper. Add mint, taste and adjust with more lemon, salt, or pepper, and then add 1/4 cup olive oil.
Grill, broil, or toast bread on both sides. Spread fresh cheese onto each toast and arrange on plates. Tumble peas onto each toast, pressing lightly so that most of peas stick to cheese.
Finish with a nice shower of grated Parmigiano and a thin ribbon of olive oil.