Add onion, carrot and garlic to a food processor, and pulse until minced. Don't go overboard here. You don't want to process it into a watery puree.

Warm olive oil in the base of a pressure cooker over medium heat, then add the minced onion mixture and a pinch of kosher salt. Cook, stirring occasionally, until the onions turn translucent (about 5 minutes). Add the crushed tomatoes, stirring to combine. Secure the lid on the pressure cooker, then cook the vegetables at a gauge of pressure of 1 bar / 15 psi for 45 minutes.

When using a pressure cooker, you want to start timing when full pressure has been reached. After you put the lid on, continue cooking the mixture over medium heat. Once the indicator pops up, start timing the 45 minutes, and continue cooking over medium flame for 5 minutes. Drop the heat to medium-low and finish cooking at the lower temp. If the indicator goes down at any time during the 45 minutes (meaning the cooker is no longer at full pressure), you'll need to increase the heat until the indicator pops up again. You'll really have to pay attention the first time you do this to get a good feel for what heat level will maintain steady pressure. It will vary based on your range. But once you figure it out, you can easily walk away while the sauce cooks.

Depressurize the cooker by letting it cool (slow method) or running lukewarm water over the rim (fast method), and remove the lid. Add a drizzle of extra virgin olive oil and a handful of chopped basil and parsley, stirring to combine.