Cook the fettuccine according to package directions. With about three minutes left in pasta cooking time, add in the peas. Once pasta and peas are fully-cooked, drain and set aside.
Heat the olive oil in a large skillet over medium high heat. Add in the garlic, and cook until just tender and fragrant, about three minutes. Add in the butter.
Once the butter is melted, stir in the flour, and cook, continuing to stir, for two minutes.
Whisk in the half and half and milk. Reduce heat to medium low, and stir constantly until thick. Add in the nutmeg and spinach. Continue cooking just until spinach is wilted, about a minute. Then remove pan from heat.
Stir in the cheese until melted, and then add in the lemon juice and zest, salt and pepper. Add in the pasta and peas, and toss until well-coated. Serve immediately topped with extra Parmesan.