Directions
Place a large pot, 6-8 quart, of water on to boil for pasta.
Select 3 large serving bowls.
Halve the cherry tomatoes, I fill a deli lid with tomatoes, set another lid on top and halve with a sharp knife so I can halve 12 or more at a time. Heat a deep skillet or saucepan over medium heat, add 3 T EVOO, 3 turns, and 2 T butter, add sliced garlic and swirl 2 minutes, add tomatoes and raise heat a bit, season with salt add a few leaves of torn basil, cover and cook sauce to collapse the tomatoes 20 minutes, stirring occasionally.
To a food processor add the juice of a lemon, 2 cloves crushed garlic, salt and pepper, 2 packed cups basil leaves and pistachio nuts, pulse to finely chop then stream in EVOO. Add 1 cup grated Parmigiano-Reggiano cheese and pulse 2-3 more times to combine, transfer to a large serving bowl.
Salt pasta water and drop pasta which you will cook 1 minute less than package directions, for pici it will be 17-18 minutes, for bucatini it will be 7-8.
Place a large skillet over medium heat with about ½ cup EVOO. Add 1 tablespoon very coarse black pepper to heat and infuse its flavor into the oil.
Remove 2 cups of starchy cooking water from pasta when it's nearly done.
Add 1 cup starchy water from pasta to black pepper oil and let it boil in the oil, whisk to emulsify. Add 1/3 of the pasta and toss with 1 ½ cups of pecorino, tossing vigorously with tongs to coat the pasta. Transfer to a bowl and top with ½ cup cheese and more pepper. For richer, sweeter preparation butter can be added to oil or heavy cream to the emulsified oil and water mixture.
Add 2/3 cup cooking water to pesto and toss with 1/3 of the pasta and vigorously toss with tongs 1 minute, wipe edges of bowl.
Add 1/3 cup cooking water to tomato sauce and add pasta and 1 cup Parm, toss with tongs 1 minute, transfer to serving bowl and top with a few more leaves torn basil.