Preparation:

1. Soak the dried tomatoes: Place the dried tomatoes in a bowl and cover them with boiling water. Let them soak for about 15 minutes until they become soft. Drain the tomatoes and pat them dry with a paper towel.

2. Toast the pine nuts: In a dry skillet over medium heat, toast the pine nuts until they turn golden brown and release their aroma. Stir them frequently to prevent burning. Remove from heat and let them cool.

3. Blend the ingredients: In a food processor or blender, combine the soaked dried tomatoes, toasted pine nuts, garlic cloves, grated Parmesan cheese, grated Pecorino cheese, and fresh basil leaves. Pulse a few times to break down the ingredients.

4. Add olive oil: While the food processor is running, gradually pour in the extra virgin olive oil in a steady stream. Continue blending until the mixture reaches a smooth and creamy consistency. If needed, you can adjust the consistency by adding more olive oil.

5. Season and store: Taste the pesto and season with salt and pepper according to your preference. Transfer the pesto to a jar or airtight container and store it in the refrigerator. It can be kept for up to a week.

6. Serve: Dried tomato pesto can be used in various ways. It can be tossed with cooked pasta, spread on toasted bread or crackers, used as a topping for grilled meats or vegetables, or incorporated into other recipes like salads or sandwiches. Enjoy its fresh and aromatic flavors!

Note: If you prefer a smoother texture, you can soak the dried tomatoes in olive oil instead of water. Additionally, you can adjust the quantity of olive oil used to achieve the desired consistency of the pesto.