Homemade Tomato Soup

4 ears of corn, husked
1 quart low-sodium chicken broth, vegetable broth, or water, plus more as needed
Kosher salt
4 tablespoons olive oil or butter
1 to 2 cups cubed zucchini or summer squash
½ cup chopped onion
¼ cup chopped scallions
½ cup chopped celery
1 garlic clove, finely chopped (plus more, to taste)
Freshly ground black pepper
1 to 2 cups cubed, peeled Yukon gold or red-skinned potatoes
1 to 2 cups cubed tomatoes
About ½ cup finely sliced fresh basil leaves

Cut the kernels off the corncobs and set the kernels aside. Place the reserved cobs in a pot with 1 quart of the broth or water, along with a teaspoon of salt. Bring the pot to a simmer over medium heat and cook until reduced to about 6 cups, about 45 minutes.
While the broth simmers, heat 2 tablespoons of the olive oil or butter in a medium skillet over medium heat. Add the zucchini or squash in a single layer, season with a pinch of salt, and let cook, undisturbed, for about a minute, until lightly browned; flip and cook the other side until browned and slightly tender but not mushy. Set aside.
In a large soup pot or Dutch oven, heat the remaining oil or butter over medium heat. Add the onions, scallions, celery, and garlic. Season lightly with salt and pepper.
When the corn broth is ready, strain it and measure to see if you have 6 cups; if not, add more broth or water, then add to the soup pot, along with the potatoes and 2 teaspoons of salt. Bring to a simmer and cook until the potatoes are tender, but not mushy, 15 to 20 minutes.
Add the tomatoes, sautéed zucchini, and reserved corn kernels and simmer until all the vegetables are heated through. Taste and adjust seasoning as desired.
To serve, divide the basil among soup bowls and ladle the hot soup on top.