Begin by cooking the fettuccine. In a large pot of salted boiling water, add the fettuccine and cook according to the package instructions until al dente, typically around 8-10 minutes. Reserve 1 cup of pasta water, then drain the noodles in a colander and set aside.
In the same large pot or a large skillet, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, but do not let it brown.
Lower the heat and pour in the heavy cream, stirring to combine. Allow it to simmer for 2-3 minutes, bringing it to a gentle bubble.
Gradually whisk in the grated Parmesan cheese, continuing to mix until the cheese has melted and the sauce is smooth. Season the sauce with salt, black pepper, and nutmeg.
Add the cooked fettuccine to the sauce, tossing to coat the pasta evenly. If the sauce is too thick, add some reserved pasta water a little at a time until you reach the desired consistency.
Gently fold in the lump crab meat, being careful not to break up the pieces too much. Cook for an additional 2-3 minutes to warm the crab.
Remove from heat and serve immediately, garnished with chopped parsley.