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Step 1
Bring 2 quarts of water to boil in a large pot. We want the starches in the pasta water to be concentrated to help our sauce later to avoid overfilling the pot with water. Add a healthy pinch of salt to the water. Do not add the pasta yet!
Step 2
Get started on the sauce while the water is coming to a boil. Heat your olive oil over medium heat in a large pan (large enough to hold all of the pasta), such as an extra-large skillet or even a wok. Then, add your sausage by tearing off small pieces and putting them in the skillet (about a teaspoon in size). Lightly brown the sausage, then remove it to a plate with a paper towel. Remove excess fat from the pan; you want to leave 1 to 2 tablespoons in the pan.
Step 3
Add the shallots and a small pinch of salt. Cook until soft, stirring constantly. Add the sliced garlic and cook for 1 to 2 more minutes (until fragrant). Add the tomato paste and cook for 2 to 3 minutes. Add the vodka and cook until it almost completely evaporates.
Step 4
Now add your pasta to the boiling water, stirring often.
Step 5
While the pasta cooks, add the cream to the sauce and turn the heat to medium-low. Mix it well and bring it to a low simmer. Add the crushed red pepper and check for heat. Don't oversalt here because we're going to add salty pasta water.
Step 6
When the pasta is almost done (slightly under al dente), use a slotted spoon or spider to scoop the pasta out of the water and into the sauce. It is OK if some water gets into the sauce; it will help emulsify our sauce.
Step 7
Mix the pasta into the sauce. Add more pasta water using a ladle, about 1/4 cup at a time. It is OK for the sauce to appear a bit thin. Let it all return to a low simmer and cook until the pasta is done to your liking — about 3 to 4 minutes. Add more water if the sauce dries out and gets tight before the pasta is done.
Step 8
Remove the pasta pan from the heat. Add the butter and sausage, and stir it in. Then add some of the pecorino romano cheese (start with half) and mix it in. Taste and add more cheese, salt or red pepper as needed. If it gets too thick or tight, add more pasta water to thin it out. Finish with basil and a pinch of the remaining cheese.