This pasta can be eaten right away or made ahead and served cold or at room temperature.
In a large pot of boiling salted water, blanch 3 garlic cloves 2 minutes. Remove garlic; set aside.
In same water, cook 1 pound linguine 5 minutes; add 1 medium russet potato, peeled and cut into 1/2-inch chunks. Cook until pasta is al dente, according to package instructions. Add 1 1/2 cups frozen peas; drain.
Meanwhile, in a blender, puree reserved garlic with 1 1/2 cups fresh basil leaves, 1/4 cup olive oil, 3 tablespoons pine nuts, and 1 cup water; season generously with coarse salt. In a large bowl, toss with pasta mixture and 4 ounces crumbled goat cheese. Garnish with more basil leaves.