Preheat oven to 400°F. Slice the baguette on a slight diagonal into 1/3-inch slices; place on a baking sheet. Pour the oil into a small ramekin and place the garlic clove in it. Use the oil to brush on both sides of the crostini, then bake for 10 minutes, or until pale golden.
Meanwhile, bring about an inch of water to a simmer in a medium saucepan and cook the fava beans or edamame for 3 to 4 minutes. Drain in a colander and run under water to stop them from cooking. If you’re using fava beans, peel off their tough outer skins.
In the bowl of a food processor, pulse the peas, arugula, Parmesan, olive oil, lemon zest and juice and garlic until well blended. If you’d like it smoother and looser, add more olive oil. Season with salt and pepper, if needed.
Spoon the arugula mixture onto the crostini and top with small leaves of (or finely chopped) fresh mint. Serve immediately.