Wash and dry all produce.
Preheat the oven to 450°F.
Halve Brussels sprouts. Peel, then cut carrot into 1/4-inch rounds. Cut potatoes into 1/2-inch pieces. Roughly chop the red onion into 1/2-inch pieces. Peel, then mince or grate garlic.
Add potatoes, Brussels sprouts, carrots, half the onions, half the garlic, half the thyme and 1 tbsp oil on a baking sheet. Season with pepper and half the garlic salt, then toss to combine. Arrange evenly into a single layer. Roast in the middle of the oven, stirring halfway through cooking, until golden-brown, 20-24 min.
While veggies roast, pat chicken dry with paper towels. Add chicken, remaining thyme, remaining garlic salt and 1 tbsp oil to a large bowl. Season with pepper and toss to coat. Heat a large non-stick pan over medium-high heat. When hot, add 1 tbsp oil, then chicken. Cook, until golden-brown, 2-3 min per side.
Remove the pan from heat. Transfer chicken to the baking sheet, on top of veggies. (NOTE: Give the veggies a stir before adding the chicken.) Roast in the middle of the oven, until chicken is cooked through, 10-12 min.
While veggies and chicken roast, heat the pan from the chicken over medium heat. When hot, add 2 tbsp butter, remaining onions and remaining garlic. Cook, stirring often, until onions soften, 2-3 min.
Sprinkle the flour over the onions and cook for 1-2 min. Add chicken broth. Cook, stirring often, until sauce slightly thickens, 4-5 min.
Remove pan from heat, then stir in sour cream.
Thinly slice chicken. Divide veggies and chicken between plates. Spoon pan sauce over top.
