Bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente.
Carefully reserve 0.25 cup of the starchy pasta water before draining the noodles.
Pat the shrimp dry with paper towels and season evenly with sea salt, black pepper, and red pepper flakes.
Heat the olive oil in a large skillet over medium-high heat.
Add the shrimp to the skillet in a single layer and sear for 2 minutes per side until pink and opaque, then remove and set aside.
In the same skillet, reduce heat to medium and add the minced garlic, sautéing for 30 seconds until fragrant.
Add the baby spinach to the skillet and toss for 1 minute until just wilted.
Return the cooked linguine and seared shrimp to the skillet.
Sprinkle the parmesan cheese over the pasta and pour in the lemon juice and reserved pasta water.
Toss everything together vigorously until the cheese melts into a light, creamy sauce that coats the noodles.
Garnish with freshly chopped parsley and serve immediately.