Peel and grate 2 large carrots on the large holes of a box grater (about 2 cups); dice 2 large celery stalks (about 1 ¼ cups); quarter and thinly slice 1 medium yellow onion (about 1 cup); trim the root end and the dark green tops from 1 large leek and remove the outer leaves, then halve the leek lengthwise and rinse the cut sides under running water to remove any sediment, and thinly slice crosswise (about 1 ½ cups).

Grate 4 to 6 whole dill pickles on the large holes of the box grater into a second medium bowl until you have 1 packed cup. Peel 1 pound Yukon gold potatoes if desired, then cut into ½-inch pieces (about 3 cups), and add to the bowl. Finely grate or mince 4 garlic cloves and add to the bowl.

Melt 3 tablespoons unsalted butter in a medium Dutch oven or heavy-bottomed pot over medium-high heat. Add the carrot mixture and cook, stirring occasionally, until starting to soften, about 4 minutes. Add the potato mixture and cook until onions are lightly browned in spots, 4 to 5 minutes more.

Add 1 (48-ounce) carton low-sodium chicken or vegetable broth, 1 cup of the dill pickle brine, 2 fresh or dried bay leaves, and ½ teaspoon black pepper. Bring to a boil. Reduce the heat to maintain a simmer and cook until the potatoes are tender, 15 to 20 minutes. Meanwhile, pick the fronds from 1 medium bunch fresh dill until you have 2 loosely packed cups.

Transfer 1 cup of broth from the soup to a bowl, add ½ cup sour cream, and stir until smooth. Return the sour cream mixture to the soup. Remove the pot from the heat. Add the remaining ¼ cup dill pickle brine and 2 teaspoons distilled white or white wine vinegar, and stir to combine. Taste and season with kosher salt and more black pepper as needed.

Top each serving with a dollop of sour cream, black pepper, and a generous sprinkle of fresh dill. Serve with rye bread if desired.