In a large skillet, melt the butter over medium-high heat.
Add the minced garlic and cook for 1 minute. Season with salt and pepper.
Add the broth, milk, and lemon zest, stirring to combine.
Add the spaghetti, pressing it down until it is covered by the liquid.
Bring the mixture to a boil, then reduce to a simmer. Cover and cook for 10 minutes.
Stir well and remove the lid, cooking another 8 minutes, until the pasta is cooked al dente and the liquid is mostly absorbed.
Stir in the kale, and cover, cooking until the kale is wilted, about 2 more minutes.
Stir in the Parmesan cheese until melted.
Serve topped with additional Parmesan cheese, if desired, and enjoy!