Add olive oil, parsley stems, and garlic to pan on medium high heat. Fry for 2 minutes ensuring not to burn, adjust heat if necessary.
Add in anchovy fillets and fry, stir occasionally until anchovies are fully broken apart, and are combined in the olive oil.
Salt pot of boiling water, and throw in spaghetti. If the cooking instructions on the spaghetti packaging says that al dente is 9 minutes, you will only be cooking the pasta in the pot of water for 6 minutes.
Remove parsley stem, and add a ladle of pasta water, ensuring a slow rolling boil. Adjust heat as necessary. Add in basil stem with leaves intact.
After 6 minutes of spaghetti cooking, remove from pasta water and add to the anchovies and garlic pan, preferably with tongs or cooking tweezers.
Mix the spaghetti to combine, and then add in another ladle of pasta water. You'll be finishing the pasta off and cooking it in the anchovy sauce as you would do with risotto. Continue to add pasta water until spaghetti is cooked, and a nice sauce is created from the emulsion of oil and starchy pasta and water.
Remove basil stem, and sprinkle in a good portion of chopped parsley. Quick mix, then add in the halved cherry tomatoes. Mix again. Check sauce, and add more pasta water if needed. Add chopped pepper if desired.
Plate your dish, garnish with more parsley, basil and hot pepper. Optional, you can add cheese.