Cook pasta according to package directions, omitting salt and fat. Add beans to pan halfway through cooking time. Drain well.
Melt butter in a medium saucepan over medium heat. Add flour, stirring with a whisk. Gradually add milk; cook until slightly thick and bubbly (about 8 minutes), stirring constantly with a whisk. Add 3/4 cup grated Parmesan cheese, salt, black pepper, red pepper, and garlic, stirring until the cheese melts. Keep warm.
Combine pasta mixture, spinach, kale, and mint in a large bowl. Stir in milk mixture, tossing gently to coat. Spoon 1 1/2 cups pasta mixture onto each of 6 plates; top each serving with 2 teaspoons shaved Parmesan cheese. Serve immediately.