Spices, wine, and a whole lotta garlic add up to a super-tasty red sauce with some heat.
Heat a large pot of water to boil for pasta.
Place a deep skillet over medium-low to medium heat and add EVOO or olive oil, about 1/3 cup, 6 turns of the pan in a slow, light stream. Add garlic and salt it, cook 12-15 minutes, flipping with a fork or tongs occasionally, until very tender and lightly caramelized. (The garlic should easily mash up with a fork.) Add thyme and sweet and hot paprika or sweet paprika and red chili flakes, and stir a minute, then add wine and reduce a minute more, and add tomatoes and bring to a bubble, then reduce heat to low and simmer 15-20 minutes.
Salt pasta water and cook pasta 1-2 minutes less then package directions. Add about ½ cup salty cooking water to sauce, then stir in cream or butter. Drain pasta. Wilt greens into sauce, if using, toss with pasta and cheese to combine, and serve in shallow bowls. Top with more cheese.