Place the guanciale in a 1-quart saucepot with 2 tablespoons of the oil and render the fat out on low heat (you don't want too much heat, or you'll scorch the guanciale), 15 to 20 minutes. When the fat is rendered out, place the guanciale on paper towels, reserve the fat and put aside.
If your tomato sauce isn't silky smooth, put it in a blender for about a minute. Add 2 tablespoons of the guanciale fat, the remaining 1 tablespoon oil and the garlic to an 8-inch saute pan. Heat it over medium-high heat to infuse the oil with garlic flavor, about 2 minutes.
Meanwhile, season the pasta water with salt and add the pasta. Cook it for 80 percent of the way (if the directions say boil for 10 minutes, boil for 8 minutes, as you will finish cooking it in the sauce).
Add the tomatoes, 1/4 cup pasta water and red pepper flakes. Remove the garlic and add a pinch of salt. Reduce for 3 to 4 minutes, then add the pasta (once it's ready) and half of the guanciale. Toss and stir for about 2 minutes (the sauce should reduce a little and the pasta should be al dente). Toss to combine and cook to bring the flavors together, about 1 minute. Turn off the heat and finely grate about 1/4 cup cheese over top.
Place the pasta onto plates. Place the remainder of the crispy guanciale on top as garnish, more cheese if necessary and a drizzle of oil. Serve immediately.