Heat half of the oil in a large skillet over medium heat. Add the onion, salt, and cook, stirring, until softened, 4-5 minutes. Add the shredded Brussels sprouts and stock and cook over medium high heat until liquid reduces by half, 4-5 minutes.
Add the Brussels sprouts leaves, season with salt and pepper to taste, toss to combine and keep warm. Cook the Tortellini according to package instructions and drain, reserving a little of pasta cooking water. Add the Tortellini to skillet and gently toss; add half of the cheese and remaining oil and gently toss again, adding the reserved pasta cooking water a little at a time to loosen the sauce if needed.
Divide Tortellini among plates. Garnish with extra cheese shavings if desired and serve.