Preheat the oven to 350 degrees Arrange the bread slices on a parchment-lined baking sheet and rub with the cut sides of the garlic, then brush with olive oil. Bake until the edges of the bread turn golden, about 10 minutes.
Meanwhile, bring a medium pot of salted water to a boil. Add the peas and cook for 2 minutes. Drain in a colander, run cold water over the peas, then drain well.
In a food processor or blender, puree the cooked peas, the 1/4 cup of olive oil, the lemon juice and mint until a coarse paste forms. Season to taste with salt and pepper; add more olive oil if the mixture is too thick.
Spread the puree over the toasts and top with Parmesan shavings.