Bring a large pot of salted water to a boil. Cook chickpea pasta according to package directions until 1 minute shy of al dente. Reserve 1/2 cup of pasta water, then drain well.
While pasta cooks, heat olive oil in a large skillet over medium heat. Add minced garlic and red pepper flakes (if using), sauté for 30 seconds until fragrant. Stir in chopped sun-dried tomatoes and cook for 2 minutes.
Pour in heavy cream, then add lemon zest and lemon juice. Season with a pinch of salt and pepper. Let the sauce simmer gently for 3–4 minutes, stirring occasionally, until slightly thickened.
Add fresh spinach to the skillet in batches, stirring until just wilted, about 1–2 minutes.
Turn off the heat. Add the drained chickpea pasta and Parmesan cheese to the skillet. Toss well, adding reserved pasta water a tablespoon at a time until the sauce coats the pasta evenly and is creamy.
Divide among bowls, top with torn basil and an extra sprinkle of Parmesan. Serve immediately with a lemon wedge.