Heat olive oil in a large Dutch oven or stockpot over medium heat. Add chicken breasts and brown for 4 minutes per side. Remove chicken and set aside on a plate (it will finish cooking later).
In the same pot, add the diced onion, carrots, and celery. Sauté for 6-8 minutes until the vegetables are softened and the onions are translucent.
Add the minced garlic and cook for 1 minute until fragrant. Stir in the rinsed wild rice, chicken broth, water, chicken bouillon base, thyme, rosemary, and the bay leaf.
Place the chicken breasts back into the pot. Bring the liquid to a boil, then immediately reduce the heat to low. Cover and simmer for 45 to 50 minutes, or until the wild rice grains have 'popped' and are tender.
Remove the chicken breasts to a cutting board and discard the bay leaf. Use two forks to shred the chicken into bite-sized pieces, then stir the chicken back into the soup.
While the soup finishes simmering, prepare the creamy base in a separate medium saucepan. Melt the butter over medium heat, then whisk in the flour and cook for 2 minutes to remove the raw flour taste.
Gradually whisk in the whole milk and heavy cream. Continue whisking constantly for 5-7 minutes until the mixture thickens into a smooth, heavy cream sauce.
Slowly pour the cream sauce into the main soup pot, stirring constantly to incorporate. Add the lemon zest, black pepper, and salt.
Simmer the soup uncovered for an additional 5-10 minutes to allow the flavors to meld and the consistency to reach a thick, creamy state. Serve hot.