Bring a large pot of salted water to a boil for the spaghetti—this takes the longest, so start it first. While waiting, mince the garlic cloves finely and chop the fresh basil. Measure out the sun-dried tomatoes, spinach, heavy cream, vegetable broth, and grated parmesan cheese. Having everything prepped and ready will let you work quickly once the sauce comes together.
Once the water is boiling, add the spaghetti and cook according to package directions until al dente (usually 8-10 minutes). Reserve 1/2 cup of pasta water before draining—this starchy liquid will help the sauce cling to the noodles. Drain the pasta and set aside.
Heat the olive oil in a large skillet over medium heat. Add the minced garlic and cook for about 1 minute, stirring constantly, until fragrant but not browned—burnt garlic will taste bitter. Add the sun-dried tomatoes and cook for another minute to warm them through and release their flavor into the oil. This quick infusion creates the foundation for a deeply flavored sauce.
Add the spinach to the pan and stir until it wilts completely, about 2 minutes. Pour in the heavy cream and vegetable broth, stirring to combine everything evenly. Lower the heat to medium-low and let this simmer gently for 2-3 minutes so the flavors meld together. I always simmer for a minute or two even after the spinach is wilted—it allows the cream to absorb the tomato flavor more fully.
Reduce the heat to low and stir in the grated parmesan cheese until it melts completely into the sauce—keeping the heat low prevents the cream from breaking or becoming grainy. Add the cooked spaghetti from Step 2 to the sauce, tossing gently to coat every strand. Add splashes of the reserved pasta water as needed to reach your desired sauce consistency; the starch will help thicken it slightly as well.
Taste the dish and season with salt, black pepper, and red pepper flakes to your preference. Stir in most of the fresh basil from Step 1, reserving a little for garnish. Divide into bowls and top with additional grated parmesan and remaining basil. I like to add a small pinch of red pepper flakes just before serving for a subtle heat that complements the sweetness of the sun-dried tomatoes.