Bring a large pot of salted water to a boil. Cook whole wheat pasta according to package directions until al dente. Reserve 1 cup pasta water, then drain pasta and set aside.
While pasta cooks, add drained roasted red peppers, 2 tablespoons olive oil, garlic, smoked paprika, red pepper flakes (if using), and a pinch of salt to a blender. Blend until smooth, adding 2–3 tablespoons pasta water to reach a creamy consistency.
In the same pasta pot or a large skillet, heat 1 tablespoon olive oil over medium heat. Add spinach in batches, stirring until just wilted, about 2 minutes. Return drained pasta to the pot, pour in the red pepper sauce, and toss to coat. Add reserved pasta water a splash at a time until sauce clings nicely to the pasta.
Remove from heat. Fold in half the feta and half the basil. Season with salt and black pepper to taste. Transfer to a serving bowl, top with remaining feta, basil, and drizzle with remaining 1 tablespoon olive oil.