Preheat oven to 425°. In a Dutch oven heat 2 tbsp olive oil over medium heat. Add shallots and cook for 1-2 minutes until starting to soften. Add in carrots, beets, sage, 1 tsp salt, and 1/2 tsp pepper and cook, stirring occasionally, for 5-6 minutes until vegetables are starting to soften. Add in barely and cook for 1-2 minutes. Stir in wine then chicken broth.
Increase heat to high and bring to a boil. Reduce heat to low, cover and simmer for 15 minutes.
Meanwhile pat chicken dry and place on a large cutting board. Remove anything from the inner cavity. Place chicken breast-side-down and use kitchen shears to cut along both side of the back bone to remove it. Flip the chicken over and press down firmly in the center of the breasts to flatten the bird. Rub chicken with olive oil and season generously with salt and pepper. Sprinkle thyme over the top.
Remove lid from Dutch oven after 15 minutes and give the pilaf a stir. Place chicken breast-side-up on top of the pilaf. Scatter lemon wedges around the chicken. Transfer to oven and cook for about 45-60 minutes until chicken is 160-165° in the thickest part of the thigh and breast.
Remove chicken to a cutting board and allow to rest for 10 minutes before carving. Stir together barely pilaf and adjust seasoning with salt and pepper as desired.