In a large dutch oven or soup pot, heat 2 tablespoons of olive oil over medium heat.
Add chicken and season with salt and pepper.
Sauté chicken until no longer pink and cooked through. Remove from pot and set aside.
Add butter and 2 tablespoons of olive oil to same pot.
Add diced onions, carrots, and celery.
Sauté until onions are tender and translucent.
Add garlic and sauté until the garlic is fragrant, about 1-2 minutes.
Add chicken back to the pot and sprinkle it all with flour.
Stir to combine everything, and cook for 2-3 minutes to remove the raw flour taste.
Slowly add in the chicken stock, while stirring and scraping the bits from the bottom of the pot.
Gently and slowly add potatoes and bay leaf to the pot. Stir to combine.
Bring stew to a boil, then reduce heat to low and simmer partially covered until potatoes are tender, about 15-20 minutes.
Stir in frozen peas and corn.
Let simmer another 10-15 minutes.
Remove bay leaf. Season with salt and pepper to taste.