1. Bring a large saucepan of water to a boil; add salt. Add squash and cook until fork-tender, about 3 minutes. Drain in a colander and transfer to a bowl of ice and cold water to cool. Drain and horizontally slice off tops of squash, keeping each top with its bottom. Cut a thin slice from bottom of each squash (to stand upright) and place on a tray.
2. Pulse together peas, cheese, 1/2 tablespoon oil, and the juice in a food processor until almost smooth. Transfer to a bowl and stir in mint; salt and pepper to taste, for pea filling.
3. Pulse together mushrooms and shallots in a clean food processor bowl until finely chopped. Heat remaining 1 tablespoon oil in a medium nonstick skillet over moderate heat. Add mushroom mixture and cook, stirring occasionally, until liquid has evaporated, about 3 minutes. Transfer mixture to a bowl and stir in cream; salt and pepper to taste, for mushroom filling.
4. Spoon pea filling onto half of squash bottoms, then top with lids. Garnish each with a mint leaf. Repeat with mushroom filling and remaining squash. Serve at room temperature. Makes 16 servings.