Start the soup: Set a large heavy pot or Dutch oven over medium heat. Add the olive oil.

Put the chopped onion, diced carrots, and diced celery into the pot. Add 1/2 teaspoon of the kosher salt and cook for 6 to 8 minutes, stirring a few times, until the vegetables look softened and glossy.

Add the sliced garlic and bay leaf to the pot. Cook for 1 minute, stirring, until the garlic smells fragrant.

Add the rinsed split peas to the pot. Stir for about 30 seconds so the peas are coated with the oil and vegetables.

Pour the chicken broth into the pot. Raise the heat to high and bring the soup to a boil.

When the broth reaches a full boil, lower the heat to medium-low so the soup bubbles gently. Partly cover the pot and cook for 35 minutes.

Stir the soup well, scraping the bottom of the pot so the split peas do not stick. Put the cover back on loosely and keep simmering.

Prep the finish: While the soup simmers, pull the meat from the rotisserie chicken if needed and shred it into bite-size pieces until you have 2 cups.

Zest the lemon, then cut it and squeeze out the juice into a small bowl. Chop the dill and keep it nearby.

After the soup has simmered for about 45 to 50 minutes total, uncover the pot and check the split peas. They should be very soft and starting to fall apart, and the carrots should be tender.

Use the back of a wooden spoon to mash some of the split peas against the side of the pot. This thickens the broth a little more.

Put the shredded chicken into the pot. Stir it into the soup and cook for 3 to 4 minutes, until the chicken is heated through.