Bring water to a boil in a 4-quart / 4L pot. Salt it generously, then add the pasta.
Cook the pasta according to package directions until al dente, about 9 to 11 minutes. Scoop out 1 cup (240 ml) of the starchy cooking water before draining, then drain the pasta in a colander.
While the pasta cooks, whisk the tahini, lemon juice, lemon zest, minced garlic, olive oil, salt, and black pepper together in a large mixing bowl. The mixture will look thick and grainy at first, that's normal.
Add 3 tbsp of the hot reserved pasta water to the tahini mixture and whisk again until it turns smooth and pourable. Add another tablespoon of warm water if it still looks clumpy.
Add the drained hot pasta directly to the bowl with the sauce. Toss well with tongs so every strand gets coated.
Add the baby spinach and toss again. The heat from the pasta wilts it within a minute or two.
Loosen the pasta with more reserved pasta water, a tablespoon at a time, until the sauce clings to the noodles but still moves when you shake the pot.
Taste and adjust with more salt, lemon juice, or red pepper flakes if using.
Divide among bowls and serve right away.