Fill a large pot with water and bring it to a boil.
Add the angel hair pasta and cook according to package directions until tender, about 5 to 7 minutes.
Reserve 1 cup of pasta water before draining the pasta. Set the pasta water aside.
Drain the pasta and keep warm.
Pat the shrimp dry with paper towels.
Mash the garlic with a pinch of salt using a mortar and pestle, or finely mince it.
Heat the olive oil and butter in a large nonstick skillet over high heat.
Arrange the shrimp in a single layer in the skillet.
Cook for 1 to 2 minutes until the shrimp begin turning pink.
Move the shrimp slightly to one side and add the garlic to the skillet.
Flip the shrimp and cook for another minute.
Squeeze the lemon juice over the shrimp.
Cover the skillet and cook for 2 to 3 minutes until the shrimp are fully cooked.
Remove the shrimp from the skillet and set aside.
Reduce the heat to medium.
Add the spinach and 1 cup of reserved pasta water to the skillet.
Cover and cook for about 1 minute until the spinach wilts.
Add the cooked pasta, Parmesan cheese, and shrimp back to the skillet.
Toss everything together until evenly coated in the lemon garlic butter sauce.
Garnish with fresh parsley and serve immediately.