Cook the pasta. Bring a large pot of well-salted water to a boil. Cook the pasta 1 minute short of the package’s al dente time it’ll finish cooking in the sauce. Before draining, scoop out about ½ cup of the starchy pasta water and set it aside.

Dry the spinach really dry it. While the pasta cooks, take your thawed spinach and squeeze it in batches inside a clean kitchen towel or several layers of paper towel, twisting hard until no more water comes out. It should feel dense and almost dry to the touch. This is the one step people skip, and it’s the difference between a sauce that stays glossy and one that turns thin and watery halfway through dinner frozen spinach holds an enormous amount of water, and if it goes into the pan wet, that water has nowhere to go but into your sauce.

Build the base. Heat the olive oil and butter together in a large skillet over medium heat until the butter’s foaming. Add the garlic and cook for about 30 seconds, just until fragrant don’t let it brown, or it turns bitter fast.

Add the spinach and artichokes. Stir in the dried spinach and chopped artichoke hearts. Cook for 2–3 minutes, stirring occasionally, until any last bit of moisture has cooked off and the spinach smells nutty rather than grassy.

Melt in the cream cheese. Reduce the heat to medium-low and add the cream cheese in a few chunks. Stir slowly and consistently it’ll look separated and weird for about a minute before it smooths out. Pro tip: if it’s fighting you, splash in a tablespoon of the broth to loosen it; the extra liquid helps it emulsify instead of clump.

Pour in the cream and broth. Add the heavy cream and remaining broth, stirring until the sauce is smooth and gently simmering. Let it bubble for 2–3 minutes to thicken slightly.

Melt in the cheeses. Turn the heat to low and stir in the parmesan and mozzarella a handful at a time, letting each addition melt before adding the next. Low heat matters here cheese added to a hard simmer tends to seize into rubbery strings instead of melting smooth.

Toss in the pasta. Add the drained pasta directly to the skillet along with the reserved pasta water. Toss until every piece is coated and glossy, about 1–2 minutes — this also finishes cooking the pasta the rest of the way. Season with salt, black pepper, and red pepper flakes to taste.

Serve immediately. The sauce is at its silkiest right off the heat. It’ll continue thickening as it sits, so serve promptly and stir in an extra splash of warm broth or pasta water if you’re not eating right away.