Cook pasta in a large pot of boiling lightly salted water according to package instructions. Reserve about ¼ cup pasta water, then drain.
While pasta is cooking, heat olive oil in a medium saucepan over medium heat. Add garlic; cook until fragrant.
Stir in tomato paste, adding a little water to loosen it if needed; cook until the color has deepened and no metallic taste remains, 2 to 3 minutes.
Off heat, stir sour cream into tomato paste mixture until incorporated; season with salt and pepper.
Add reserved pasta water, a little at a time, until sauce reaches desired consistency.
Toss cooked pasta into sauce until well coated. Garnish with basil to serve.
