Hors d'oeuvres can be a challenge; all too often they take a disproportionate amount of time to prepare. The components of this recipe can be made a day or two ahead, and assembled just before heating and serving. Edamame are soy beans, and they're sold in several forms: fresh or frozen whole pods, fresh shelled edamame, or frozen shelled edamame. To save prep time, buy edamame already shelled if possible.
Position a rack in the upper third of the oven and preheat to 350 degrees F.
Arrange the bread slices on a baking sheet. Lightly brush the top side of the slices with some of the olive oil. Bake until the crostini are golden brown, 12 to 16 minutes. Cool completely, then store in an air-tight container at room temperature for up to 2 days.
Place the remaining olive oil (about 1/3 cup) in a heavy-bottomed saucepan and warm over low heat. Add the garlic, cover the pan, and cook slowly until the garlic is tender and soft, on the verge of dissolving. Stir occasionally and check to makes sure the garlic doesn't brown or burn. This step should take 25 to 25 minutes.
Add the edamame and 1 cup of hot water to the garlic. Raise the heat to medium, and cook, uncovered, stirring frequently, until the edamame soften and start to disintegrate, 10 to 15 minutes.
Remove the pan from the heat and mash the garlic and edamame into a coarse purée with a fork or potato masher. Season to taste with the salt and pepper. Transfer to a small container, cover, and refrigerate for up to 5 days before using.
To serve, preheat the broiler. Spread some of the garlicky edamame purée onto each crostini. Place the crostini on a baking sheet and sprinkle them with some of the cheese. Broil until the cheese melts and turns golden, about 2 minutes. Serve immediately.