Sauté garlic. Heat 2 Tbsp olive oil in a large Dutch oven or soup pot over medium-high heat. When hot, add 3 cloves minced garlic and cook, stirring often, until fragrant, about 1 minute.
Add the liquid. Pour in 8 cups of chicken stock, then add 1 lb boneless skinless chicken thighs, 1 cup of white rice, and 2 bay leaves. Bring to a boil, then reduce heat to medium-low to medium. Simmer until chicken is fully cooked and the rice is tender, about 25 minutes.
Shred the chicken. Remove the bay leaves and discard. Transfer the cooked chicken thighs to the bowl of a stand mixer with beater attached, then beat on medium speed until chicken is fully shredded. Alternatively, you can use two forks to pull the meat. Return the chicken to the pot.
Temper the eggs. Place 3 eggs in a mixing bowl, then whisk well along with 1 tsp lemon zest and the juice from 2 lemons. Slowly drizzle in about 2 ladles of warm broth, whisking the entire time, to gently bring the eggs up to temperature without scrambling them. Drizzle and whisk the tempered egg and lemon mixture back into the chicken soup slowly.
Garnish, then serve. Bring the heat back up to medium to medium-high, then cook for about 5 minutes to thicken. Taste and adjust seasoning as needed. We recommend starting with about ½ tsp Kosher salt and working up from there (different chicken stocks vary in terms of saltiness). Serve immediately with freshly cracked black pepper, lots of fresh dill, and baguette, if wanted.