Add cottage cheese, lemon juice, and 1/4 cup of the Parmesan to a blender. Blend on high until completely smooth and silky, about 60 seconds. Scrape down the sides once if needed. The mixture should look like thick cream with no visible curds.

Bring a large pot of salted water to a rolling boil. Cook pasta until al dente according to package directions, usually 9-11 minutes. Before draining, scoop out 3/4 cup of the starchy pasta water and set aside. Drain the pasta and do not rinse.

While the pasta cooks, heat olive oil in a large skillet over medium heat. Add minced garlic and cook until fragrant and just starting to turn golden at the edges, about 90 seconds. Do not let it brown or it will turn bitter.

Reduce heat to low. Pour in the blended cottage cheese mixture, salt, black pepper, and red pepper flakes if using. Stir constantly for 2-3 minutes until warmed through and slightly thickened. The sauce should coat the back of a spoon but still be pourable.

Add the hot drained pasta directly to the skillet. Toss vigorously, adding reserved pasta water a few tablespoons at a time, until the sauce clings to every piece of pasta and looks glossy rather than gloppy. You may not need all the water. Cook together for 1 minute so the pasta absorbs some sauce.

Remove from heat. Sprinkle remaining 1/4 cup Parmesan over the top and toss once more. Divide among bowls, top with torn basil, and serve immediately with extra Parmesan on the side.