Using a metal spoon, as slowly as you can, add the 1/3 cup olive oil into the mixture 1 spoonful at a time. Then add the Parmigiano-Reggiano. If a more drizzle-friendly consistency is desired, add the remaining 2 tablespoons olive oil; otherwise, leave it as-is. Taste and, if you feel it's necessary, season with salt to taste, although given how salty Parmigiano is, you may not need any added salt. Use immediately or, to store the pesto for later, pour it into a clean jar, top with just enough olive oil to completely cover the surface, screw on the lid, and tuck it away in the fridge for up to 3 weeks.