Set a large, heavy-bottomed pot over medium heat and pour in the oil. When the oil shimmers, add the diced onions and kosher salt, stirring to coat the onions evenly. Cook for about 5 minutes, stirring from time to time, until the onions soften and turn translucent without taking on too much color.

Stir in the carrots, celery, zucchini, parsley, and garlic. Sauté this vegetable mixture for another 10–15 minutes, allowing the carrots to begin softening and the garlic to release its aroma. The vegetables should look glossy and lightly tender, forming a flavorful base for the soup.

Pour in the water and increase the heat to bring the pot to a steady boil. As the liquid heats, scrape the bottom of the pot with a spoon to lift any browned bits from the vegetables into the broth.

Nestle the chicken thighs and bay leaves into a mesh or net bag, securing it well so everything stays contained. Lower the bag into the boiling liquid, making sure the chicken is fully submerged so it cooks evenly and flavors the broth.

Once the soup returns to a boil, stir in the split pea soup mix, discarding the included flavor packets. Mix well so the peas are evenly distributed throughout the pot.

Reduce the heat to a gentle simmer. Let the soup cook for 2–3 hours, partially covered, stirring occasionally to prevent sticking. The peas should break down into a creamy consistency, and the chicken should become very tender and begin to fall off the bone.

Lift the net bag out of the pot and transfer it to a bowl. Remove and discard the bay leaves, chicken skin, and bones. Shred the cooked chicken into bite-sized pieces, then return the meat to the soup and stir to combine. Taste and adjust the seasoning if needed before serving the soup hot.