Core the tomatoes, slice them in half, and place them cut side up on a rack over a sheet tray lined with parchment paper.
Drizzle on 2 tablespoons of olive oil, season with salt and pepper, and bake on a middle rack in the oven at 475° for 30 minutes.
Set them to the side to cool to room temperature.
In the meantime, add the almonds to a large non-stick or stainless-steel skillet and cook over low-medium heat for 4 to 6 minutes while constantly stirring using a spoon or by flipping the pan just until about half of them are lightly browned. Set them aside.
Next, add the tomatoes, almonds, and cheese to a blender and blend on high until smooth.
Next, add in the ½ cup of olive oil, basil, mint, garlic, and optional balsamic vinegar, and blend on high until completely smooth with no specks of any herbs. Set it to the side.
Boil the pasta in a large pot of salted boiling water according to its package.
Drain the pasta and add it to a large bowl or pot along with ½ the sauce and toss with a ¼ cup of finely grated pecorino Romano.
Serve with additional grated pecorino Romano cheese. There will be enough sauce left over for another pound of cooked pasta. However, I usually freeze the remaining sauce.
