Put the pot on the stove, turn the heat to medium, and add the oil. When the oil is hot, add the onion, garlic, and celery and cook, stirring occasionally, until the vegetables are tender, about 10 minutes.
Add the tomatoes and their juices, the broth, and the salt. Raise the heat to high and bring to a boil.
Turn the heat down to low and cook for 30 minutes, stirring occasionally to make sure it’s not sticking. Set aside to cool for 15 minutes.
Using the slotted spoon, remove half the solids and put them in the blender. Do not fill the blender more than halfway. Put the top on the blender but remove the little cap in the center. Cover the hole with a dish towel.
Turn the blender to the lowest speed and begin to blend, then increase the speed gradually and blend until smooth. Turn off the blender, add the remaining solids from the pot, and blend again. While blending, gradually add the cooking liquid and yogurt through the hole in the lid. Use a clean spoon to taste the soup. Does it need an extra splash of vinegar or a pinch of salt? Add it and taste again.
Serve right away, or cover and refrigerate up to 3 days.