Prep and dice all the vegetables. Pound the chicken breasts slightly and season with salt, garlic powder, and pepper.
In a large, sturdy-bottom pot over medium-high heat, melt 1/4 cup butter. Add 1/2 yellow onion and 1 yellow squash. Cook for about 4 minutes, until softened. Add 5 cloves minced garlic and cook 1 minute more.
Transfer the veggies to a blender. Add 4 cups chicken broth and 1 cup almond milk. Blend until completely smooth and creamy.
In the same pot, add 2 tablespoons olive oil over medium-high heat. Sear the chicken breasts on both sides until golden brown. This step adds so much flavor.
Pour a bit of the blended broth into the pot to deglaze and scrape up the flavorful bits. Add in the remaining broth mixture. Stir in 2 teaspoons garlic powder, 1 tablespoon thyme, 1 teaspoon rosemary, 1 teaspoon salt, and 6 bay leaves.
Add 2 diced carrots, 2 diced celery stalks, and 2 peeled and cubed golden potatoes. Bring everything to a gentle boil and cook for 15 minutes until the veggies are soft.
Remove the chicken and shred it with two forks. Add it back to the pot. Stir in 1 cup peas and 1 cup corn. Simmer for 5 minutes more.
Turn off the heat and remove the bay leaves. Stir in 2/3 cup plain Greek yogurt until smooth.