-- Handful of fresh basil, plus 4-5 leaves for garnish
3/8 cup grated Pecorino Romano or Parmigiano-Reggiano cheese
-- salt, to taste
-- pepper, to taste
3/8 cup extra-virgin olive oil
Preheat oven to 400F. Halve and trim red pepper and, when oven is heated, place half skin-side down on oven rack (or use a pan if preferred). Roast 15-20 minutes, or until skin is well shriveled (but not blackened).
Place garlic cloves in medium saucepan, add cold water to cover, and bring to a boil. Reduce heat and simmer for 5 minutes or until soft enough to pierce with a fork. Remove garlic using a slotted spoon (keeping water in pan), and set aside to drain.
Meanwhile, quickly toast chopped walnuts in a warmed frying pan (without oil), stirring consistently, over medium-high heat just until they start to turn golden. Remove from heat and place on paper towels.
Place sun-dried tomatoes in saucepan containing reserved water, adding more water to cover as necessary. Bring to a boil, then reduce to a simmer. Simmer 8-10 minutes. Remove using a slotted spoon (keeping water in pan), and set aside to drain, blotting well with paper towels.
Prepare an ice bath. Blanch basil very briefly (3-4 seconds) in still-warm reserved water. Quickly transfer to ice bath. Drain and dry basil thoroughly with paper towels
Thoroughly dry all above ingredients with paper towels as necessary. Place in a blender or processor, adding 3/8 cup cheese, and salt and pepper to taste.
Blend, adding oil incrementally, until smooth and paste like.