Soak morels in warm water in a small bowl 30 minutes. Lift mushrooms out of water, squeezing excess liquid back into bowl. Pour soaking liquid through a sieve lined with a dampened paper towel into a small bowl and reserve. Rinse morels thoroughly to remove grit, then squeeze dry. Discard any tough stems. Halve small morels lengthwise and quarter larger ones. Cook asparagus and beans in a 6- to 8-quart pot of boiling salted water , uncovered, 3 minutes. Add peas and cook until beans and asparagus are just tender, about 1 to 2 minutes more. Immediately transfer vegetables with a large slotted spoon to a bowl of ice and cold water to stop cooking, reserving hot water in pot for cooking pasta. Drain cooled vegetables in a colander. Cook 1 teaspoon garlic and a rounded 1/4 teaspoon red pepper flakes in 2 tablespoons oil in a 10- to 12-inch heavy skillet over moderately low heat, stirring, just until garlic is fragrant, about 1 minute. Add drained vegetables and salt and pepper to taste and cook, stirring, 2 minutes, then transfer to a bowl. Reserve skillet. Cut half of tomatoes into quarters and halve remainder lengthwise, keeping quarters and halves separate. Cook remaining teaspoon garlic and remaining rounded 1/4 teaspoon red pepper flakes in remaining 2 tablespoons oil in skillet over moderately low heat, stirring, just until garlic is fragrant, about 1 minute. Add quartered tomatoes with salt and pepper to taste and simmer, stirring occasionally, until tomatoes are softened, about 3 minutes. Add halved tomatoes, vinegar, and water and simmer, stirring occasionally, until sauce is thickened and halved tomatoes are softened, 3 to 4 minutes. Keep tomatoes warm. While tomatoes are cooking, return water in pot to a boil and cook spaghettini until al dente. Drain in a colander. Immediately add butter, cream, zest, and morels to empty pasta pot and simmer gently, uncovered, 2 minutes. Stir in cheese and add pasta, tossing to coat and adding as much of reserved morel soaking liquid as necessary (1/2 to 2/3 cup) to keep pasta well coated. Add green vegetables, parsley, basil, pine nuts, and salt and pepper to taste and toss gently to combine. Serve pasta topped with tomatoes and Parmigiano-Reggiano shavings.