Select the “Sauté” function on the Instant Pot® and add olive oil once hot. Add onion, celery, and carrots and season with salt and black pepper, to taste. Cook, stirring occasionally, until fragrant and vegetables develop some color, approximately 4-5 minutes. Add garlic and sauté for an additional minute.
Pour in stock and deglaze the bottom of the pot, gently scraping up any brown bits off the bottom of the pot with a wooden spoon in the process. Continue cooking for 2-3 minutes before turning the unit off.
Add tomatoes, bay leaf, thyme, and rosemary, and stir to combine. Add lid and lock into place. Position the vent to “Sealing” and set the “Manual” setting to 4 minutes.
When cook time is complete, allow pressure to release naturally for 5 minutes, then manually release any remaining pressure. Remove lid and stir in fresh basil leaves.
Carefully transfer tomato mixture to a food processor or high-powered blender and process until smooth. (For chunkier results, use an immersion blender instead).
To serve, transfer soup to individual bowls while still hot and garnish with additional fresh basil, if desired. Enjoy!