Season chicken thighs on both sides with salt and pepper. In a dutch oven or large oven-safe saucepan over medium-high heat, sear chicken in oil and 1 tablespoon butter on both sides 2-3 minutes until golden. Transfer chicken to a plate and set aside.
Add remaining tablespoon butter to same skillet and then add onion, baby carrots, and potatoes. Saute in butter 5-10 minutes until lightly golden. Add garlic and saute 1 additional minute.
Nestle chicken back into pan and arrange herbs around it. Pour beer and broth into pan and bring to a low simmer. Cover pan and place in 350F oven. Bake chicken 40-45 minutes until chicken is fall-apart tender and vegetables are tender.
Remove chicken and vegetables and place on a cutting board momentarily. Discard herb sprigs. Whisk flour with a little water and add to remaining liquids in pan. Bring to a simmer over medium heat, stirring occasionally until sauce is slightly thickened.
Season sauce with salt and pepper to taste and toss vegetables and chicken back into pan until coated in sauce. Serve hot and enjoy!