Bring a large pot of water to a boil and add kosher salt. Add your pasta and cook as directed on the bag.
In a food processor, combine basil, garlic, salt, and almonds. Process until completely combined. Add in the cherry tomatoes and process while slowly pouring in the olive oil until combined and smooth. Add the parmigiano and combine.
Drain the pasta and save ½ cup of the pasta water. Add the pasta water to the pesto. Combine the pasta and the pesto. Stir well until the pasta develops a creamy texture.
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Notes
Slowly pour the olive oil into the processor so you can see how much you need. It's about a ⅓ cup, but you want the pesto to reach a mostly smooth but slightly rough texture.
Use high-quality extra virgin olive oil. With dishes that are not "cooked" like this, the simple flavors are really important to get the best out of the dish.
Use the same hot pot you used to boil the pasta! This is important to get the creamiest pasta!