Cook the shrimp. Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Season shrimp with salt and pepper, then add to the pan in a single layer.
Cook 1–2 minutes per side, just until pink, lightly charred, and opaque.
Remove shrimp from the skillet and set aside.
Boil the pasta. Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Reserve at least 1 cup pasta water, then drain.
In the same skillet, reduce heat to medium and add the remaining 3 tablespoons butter.
Add chopped onion and cook 2–3 minutes, until soft and translucent.
Add garlic and cook 30 seconds, just until fragrant.
Pour in the wine or chicken broth. Simmer 2–3 minutes, scraping up any browned bits from the pan.
Stir in the cream and bring to a gentle simmer. Add Parmesan cheese and stir until melted and smooth.
Add the cornstarch slurry and stir continuously for 1–2 minutes, until the sauce thickens and turns glossy.
Add the cooked pasta to the sauce along with ½ cup pasta water. Toss to coat.
Add more pasta water as needed to loosen the sauce and make it ultra creamy.
Return shrimp to the skillet and toss gently to combine. Cook 1–2 minutes, just until heated through.
Taste and adjust seasoning with salt and pepper.
Remove from heat and finish with chopped parsley.