Begin by bringing a large pot of salted water to a boil. Add the whole wheat angel hair pasta and cook according to the package instructions until al dente, usually about 4-5 minutes. Drain the pasta, reserving a bit of the pasta water for later use if desired.
While the pasta cooks, heat the olive oil in a skillet over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.
To the skillet, add the sliced grape tomatoes, diced artichoke hearts, and anchovy paste if using. Stir well to combine and cook for about 3-4 minutes until the tomatoes start to soften.
Next, stir in the capers, crushed red pepper flakes, black pepper, and a pinch of salt. Pour in the vegetable broth and bring the mixture to a gentle simmer. Allow it to cook for about 5 minutes, letting the flavors meld together beautifully.
Once the sauce has thickened slightly, add the baby spinach to the skillet, stirring until it wilts down. This should take just a couple of minutes.
Add the drained angel hair pasta to the skillet and toss everything together, ensuring the pasta is well coated in the sauce. If the mixture seems too dry, add a splash of the reserved pasta water to loosen it up.
Remove from heat and sprinkle the freshly chopped basil and grated Parmesan cheese over the top. Give it one last gentle toss before serving. Enjoy your Pasta Puttanesca with Baby Spinach immediately, garnished with additional cheese and fresh basil if desired.