Cook Pasta & Peas: Bring a large pot of salted water to a boil. Add tortellini and cook according to package directions. During the last 2-3 minutes of cooking, add the sugar snap peas. Before draining, reserve 1 cup of pasta water. Drain and set aside.
Sauté Aromatics: In a large skillet over medium heat, heat olive oil. Add shallot and cook for 1-2 minutes until softened. Add garlic and cook for 30 seconds until fragrant.
Make Sauce: Add chicken broth, heavy cream, salt, pepper, lemon zest, and fresh dill. Bring to a gentle boil, then reduce heat to medium low. Simmer for 2-3 minutes, stirring occasionally, until sauce thickens and coats the back of a spoon.
Add Cheese: Remove skillet from heat. Stir in ¼ cup of the Parmesan cheese until melted and smooth.
Combine: Add the cooked tortellini and snap peas to the skillet. Toss gently to coat. If sauce is too thick, add reserved pasta water, 1 tablespoon at a time, until desired consistency is reached.
Serve: Divide among bowls. Garnish with remaining ¼ cup Parmesan and extra fresh dill. Serve immediately.