Cook the pasta: Bring a large pot of salted water to a boil. Add the pasta and cook until al dente according to package directions.
Before draining, reserve 1/4 cup of the starchy pasta water. Drain and set aside.
Make the sauce: In a small bowl, whisk together soy sauce, honey, rice vinegar, sesame oil, red pepper flakes, and lemon juice. Taste and adjust the honey or lemon to balance sweetness and brightness.
Pat the shrimp dry: Use paper towels to remove moisture so they sear well.
Season lightly with salt and pepper.
Cook the shrimp: Heat olive oil in a large skillet over medium-high heat. Add shrimp in a single layer and cook for 1–2 minutes per side until pink and opaque. Transfer to a plate.
Do not overcook.
Sauté the garlic: Reduce heat to medium. In the same skillet, add the minced garlic. Stir for 30 seconds until fragrant, scraping up any browned bits.
Build the sauce in the pan: Pour in the honey-garlic mixture.
Let it bubble for 1 minute to slightly thicken.
Add pasta and greens: Toss the cooked pasta and spinach into the skillet, adding splashes of reserved pasta water as needed to loosen and help the sauce cling. Stir until the spinach wilts.
Finish with shrimp: Return shrimp and any juices to the skillet. Toss gently for 30–60 seconds to warm through and coat with sauce.
Taste and serve: Adjust seasoning with salt, pepper, or extra lemon.
Top with green onions and sesame seeds. Serve hot.