“Silk Handkerchief” Pasta with Pesto (Mandilli de Saea al Pesto Genovese)

Ingredients

• 3 1/2 cups flour
• 1/2 tsp. salt
• 5 eggs
• 2 tbsp. extra-virgin olive oil
• 1 clove garlic, peeled and chopped
• 3 tbsp. pine nuts
• Salt
• 2 cups packed fresh basil leaves, preferably small and young
• 1/2 cup extra-virgin olive oil
• 1/4 cup freshly grated pecorino sardo
• 1/4 cup freshly grated parmigiano-reggiano