Prep the Potatoes: Peel the Yukon gold potatoes. Then, evenly chop them into even-sized 1-inch pieces. Set aside.
Sauté the Veggies: Heat the olive oil in a large Dutch oven over medium heat. Add the diced onion, crushed garlic cloves, and diced red bell pepper. Sauté for 4 to 5 minutes until softened and fragrant. Then, push the veggies to one side of the pot.
Sear the Chicken: Season both sides of the chicken breasts with 1/2 teaspoon salt and 1/4 teaspoon pepper. Add them to the Dutch oven and sear for 4-5 minutes per side, until golden brown.
Add Potatoes, Corn, and Chiles: Add the peeled and chopped potatoes, frozen corn, mild green chiles, smoked paprika, thyme, and a bay leaf.
Simmer: Pour in the chicken broth and bring to a boil. Stir everything together until well combined. Reduce the heat to a gentle simmer and cook for 20 to 25 minutes, or until the chicken is fully cooked and the potatoes are tender.
Shred the Chicken: Remove the chicken from the pot and shred it with two forks on a cutting board. Set aside. Also, remove the bay leaf from the pot.
Blend for Creaminess: Use an immersion blender directly in the pot to blend part of the chowder until creamy, but still chunky. Do not fully blend the chowder. You want to keep some texture with the potatoes and corn.
Finish it Off: Stir the shredded chicken back into the pot. Then, add the milk and stir until warmed through. Taste and season with 1 to 1½ teaspoons of salt and 1/4 teaspoon of pepper, or to taste.
Serve and Enjoy: Ladle the chowder into bowls and top with your optional favorite toppings such as fresh parsley, green onions, shredded cheddar cheese, Greek yogurt, or crispy bacon.