Preheat the oven to 350°F. Spread the almonds on a sheet pan into a single layer and bake. Shake the pan and check every few minutes until the almonds are golden brown, about 3-5 minutes. Keep an eye on them to make sure that they don’t burn.
Fit a food processor with a blade. Add a ½ cup of the almonds, all of the basil, a generous handful of grated Parmesan cheese, tomatoes, garlic, and enough olive oil to mix. Pulse until roughly chopped and combined but not smooth. Add more olive oil as needed and salt to taste.
Bring a pot of salted water to a boil, and cook the penne until al dente. Reserve a ½ cup of starchy pasta water. Transfer the pasta to a saute pan and add the sauce and toss until coated. Add ¼ cup of the pasta water and cook over medium heat until warmed through. Season with salt if needed.
To serve, top with the remaining toasted almond slices and Parmesan cheese.