Bring a large pot of salted water to a boil.
Add the thawed peas to a small saucepan with butter and cream. Warm over medium heat for about 2–3 minutes until the peas are hot.
Transfer the peas to a blender with basil, mint, olive oil, salt, pepper, and lemon juice. Blend until completely smooth and silky. Add a splash of warm water or cream, as needed, to help the purée blend easily and achieve a slightly loose, saucy texture. Taste and adjust seasoning.
Cook the stuffed pasta according to the package instructions. Before draining, reserve about 1 cup of pasta water as a safety net.
In a large skillet, melt the butter over medium heat. Add the lemon juice and lemon zest and let it melt together until fragrant.
Transfer the pasta directly from the pot to the skillet. A little pasta water will come with it, which helps start the sauce.
Toss the pasta gently in the lemon butter. Add grated Parmesan directly to the pasta and continue tossing so it melts into the sauce.
Add a small handful of peas and toss briefly so they warm through without losing their vibrant color.
If the pasta looks dry, add a splash of the reserved pasta water until the sauce becomes glossy and lightly creamy.