In a large stockpot, heat olive oil over medium heat and sauté onion, carrots, and celery for 7 minutes until softened.
Add minced garlic and cook for 60 seconds until fragrant.
Whisk in the flour and cook for 2 minutes to create a light roux, stirring constantly.
Gradually pour in the chicken bone broth and almond milk while whisking to prevent clumping.
Add thyme, rosemary, salt, and pepper; bring the mixture to a gentle simmer.
Simmer for 10 minutes or until the liquid has thickened slightly and vegetables are tender.
Fold in the shredded chicken, peas, and corn, heating for an additional 5 minutes.
Remove the pot from the heat source.
Whisk a small amount of the hot soup into the Greek yogurt to temper it, then stir the mixture back into the pot until creamy.
Serve immediately, garnished with fresh herbs if desired.