Heavily salt a large pot of water (using about 1 tablespoon of the kosher salt), then bring to a boil. Add the fusilli and cook, stirring occasionally to prevent sticking, until pasta is al dente, about 1 minute less than the minimum given on the package. If using fresh peas, stir them into the pot 3 minutes before the pasta is done. If using frozen peas, add them to the pot 1 minute before the pasta is done.
Reserve ½ cup of the pasta-cooking liquid in a measuring glass, then pour off the remainder, leaving the pasta and peas in a colander to drain.
Return the empty pot to the stovetop and place over medium-high heat. Pour in the heavy cream and cook until it bubbles, thickens, and is reduced by half, about 2-3 minutes. Whisk in the cheese until it melts into the reduced cream, then stir in the chopped baby spinach to wilt. Add the ¾ teaspoon kosher salt, garam masala, freshly ground black pepper, and chile flakes (if using). Add in the drained pasta and peas, stir to cover with the cheese sauce. If you need a little more liquid, add some of the reserved pasta water. Stir in the lemon juice for a little acid punch to brighten up the flavors, taste, and adjust the seasonings to suit your tastes. Serve immediately.