Fill a large pot with water, add a generous pinch of salt, and bring to a rolling boil. Once bubbling, add the pasta and cook until al dente, about 9 minutes, stirring occasionally.
While the pasta cooks, heat olive oil in a sauté pan over medium heat. Add minced garlic and sauté until fragrant and just golden, about 30 seconds, filling the kitchen with a warm, garlicky aroma.
In the last 2 minutes of pasta cooking, add frozen peas to the boiling water. Once the pasta and peas are cooked, drain them together, reserving a cup of starchy water for later.
Add the drained pasta and peas to the sauté pan with garlic. Toss gently to coat everything in the fragrant oil, warming the mixture for about 1 minute.
Stir in a squeeze of lemon juice, followed by the lemon zest, and toss in the chopped spinach. Cook just until the spinach wilts and turns a vibrant green, about 1-2 minutes.
If the mixture appears a bit dry, add a splash of the reserved starchy pasta water. Stir gently to create a silky, cohesive sauce that coats the pasta and greens beautifully.
Taste the dish and adjust seasoning with a pinch of salt, pepper, or more lemon juice if needed. Remove from heat and sprinkle generously with freshly grated cheese.
Serve immediately while warm, garnished with extra cheese and a final squeeze of lemon for brightness. Enjoy the vibrant flavors and fresh green colors in every bite.