Turn on Instant Pot to Sauté setting and add oil. Once oil is hot, add onion. Cook, stirring occasionally, for 3 to 5 minutes until softened. Add garlic and cook another 30 seconds, until fragrant.
Deglaze the bottom of the insert by adding 1 cup broth. Scrape the bottom with a wooden spoon or spatula, making sure to get all the browned bits off the bottom. This will help you avoid the "burn" warning during cooking.
Stir in carrots, tomatoes with their juices, sugar, tomato paste, fresh herbs, and spices.
Cook on high pressure for 15 minutes. Let pressure naturally release (i.e. don't touch it!) for 10 minutes. Manually release any remaining pressure.
Use an immersion blender to blend the soup until smooth. You can also puree it in batches in the blender or food processor.
Taste and adjust seasoning as desired. I have a bunch of notes above for flavor variations! See below for tips on adjusting the consistency.**
Serve with crusty bread, grilled cheese sandwiches, and/or salad.