Combine pasta, garlic, butter, 1½ teaspoons salt, and water in a large, straight-sided skillet. Bring to a boil over high heat. Cook, stirring often, for 5 minutes. Add sugar snap peas and continue to cook until pasta is al dente and water has reduced to a sauce-like consistency, 2–3 minutes.
Quickly add peas and stir to warm through. Add mint and toss to combine. Divide among 4 bowls and top with ricotta and lemon zest. Season with salt and pepper. Serve immediately.
Combine milk and salt in a heavy-bottomed saucepan over medium heat. Warm milk, stirring often with a rubber spatula to prevent scorching, until it reaches 180°.
Remove from heat and briefly stir in vinegar and lemon juice. Let sit undisturbed while curds form, about 5 minutes.
Set a sieve over a large bowl and line with cheesecloth. Carefully transfer the curds to sieve and let drain briefly. Serve immediately or store in refrigerator.