In a food processor or in the mortar, blend or smash the garlic and almonds with 3 tablespoons of oil and a pinch of coarse salt until you have a smooth paste.
Rinse and pat the basil dry; add it to the almond paste.
Add the tomatoes and three more tablespoons of oil.
Pulse at low speed until you have a well-blended sauce. Pour in abundant (3-4 tbsp about) extra virgin olive oil and let sit.
Cook the pasta in plenty of salt water according to the package instructions.
Pour the pasta into a serving bowl; add the pesto and toss well until it has evenly coated the pasta.
Generously sprinkle with freshly grated pecorino cheese.