1. Cook pasta according to package directions. Drain and transfer to a serving bowl and toss with 1/2 Tbsp. of olive oil.
2. Heating remaining 1 1/2 Tbsp. olive oil in a skillet over medium-high heat. Add carrots, red pepper, garlic, sugar and chile flakes and saute. Stir in kale, mustard greens, asparagus and vinegar and continue to saute. Add tomatoes and season with salt and pepper. Cook until vegetables are tender. Stir in the basil in the last 2 minutes of cooking.
3. Spoon the greens mixture over the cooked pasta, toss well to combine. Top with cheese. Serve