Preheat oven to 325° Fahrenheit.
Place flour in a large bowl and toss short ribs to coat.
Pre-heat a large skillet to medium high, add 4 tablespoons oil. Brown the short ribs on all sides in batches. Place short ribs in two 9x13 pans.
Add remaining 2 tablespoons oil, carrots, and onions to pan and sauté for 2-3 minutes. Add garlic and cook until fragrant, about 1 minute. Add beer to pan and boil until volume is reduced by half. Pour 3 cups of beef stock into reduction. Season to taste with salt and pepper.
Divide mixture evenly over short ribs. Top each pan with 4 sprigs of thyme and 2 sprigs rosemary.
Cover pans with foil and place in oven. Cook for 2 ½ hours covered.
During the last hour of cooking time add root vegetables, baby potatoes, and pearl onions. Cover and return to oven until vegetables are fork tender and meat is pulling away from the bone.
If desired, when short ribs are finished cooking uncover and pour cooking liquid into a sauce pan. Boil until mixture is thickened and sauce-like. Serve over short ribs with vegetables.