Bring a medium pot of well-salted water to a boil and set up a bowl of well-salted ice water. Drop the peas in the boiling water, let the water return to a boil and cook the peas for 2 minutes. Scoop the peas out of the water and plunge them immediately into the ice water. When the peas are cool, remove them from the ice water and reserve. Repeat this process with the fava beans. When the favas are cool, peel off the tough outer layer and reserve the beans.
In a food processor, pulse the peas to make a coarse paste. In a large bowl, combine the pea paste, ricotta and parmigiano; mix well, season with kosher salt (about 1/2 teaspoon) and taste to make sure it's delicious. In a separate bowl, toss the favas with the olive oil, mint, lemon zest and a pinch of kosher salt. Set aside.
Heat a grill pan over medium-high heat. Brush both sides of the bread slices with olive oil and grill, flipping, until lightly charred, 30 seconds to 1 minute.
Spread about 1 tablespoon of the pea-ricotta mixture onto each crostini. Top with the favas, a final shaving of parmigiano, a drizzle of olive oil and a pinch of sea salt.