Make the sauce: Melt the butter in 12-inch skillet over medium-high heat. Add the shallots and ¼ teaspoon salt and cook until softened, about 2 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Stir in the wine and cook until nearly evaporated, about 2 minutes. Stir in the half-and half, peas, tarragon, and dissolved cornstarch mixture and simmer until slightly thickened, about 2 minutes. Remove the skillet from heat, cover, and set aside.
Add the asparagus and 1 tablespoon salt to the boiling water and cook, stirring often, until the asparagus is tender but still crisp at the center, about 2 minutes. Using a slotted spoon, transfer the asparagus to a large paper-towel-lined plate and set aside.
Return the water to a boil, stir in the tortellini, and cook until tender. Reserve ½ cup of cooking water, then drain the tortellini and return the tortellini to the pot.
Stir the sauce and asparagus into the tortellini. Season to taste with salt and pepper, adding the reserved pasta cooking water as needed to loosen the sauce. Serve immediately with freshly grated Parmesan and lemon wedges.