Lay all four meats on your cutting board, pat dry and salt, pepper and rosemary each side.
Preheat oven to 325 degrees F.
In a large saute pan over medium high heat, place two tablespoons of the oil and heat until the oil is shimmering.
Have a five quart Dutch oven standing by.
Cook one meat at a time in the hot oil cooking each side for about 3-4 minutes per side. Make sure the meat is not over crowded and don’t touch it until it is time to turn. Turn each piece and cook for another 3-4 minutes or until nice and browned. Transfer to the Dutch oven. Repeat for the second meat and before cooking the third meat, add the remaining oil. Save the chicken for last and only sear for about 2 minutes per side.
Once the last meat is in the Dutch oven, place the onions and garlic into the hot saute pan and cook for three minutes.
Add the red wine and scrape the pan bottom with a wooden spoon. Cook to evaporate the wine by half then add the onion and wine mixture to the Dutch oven. You are done with the saute pan.
To the Dutch oven, add tomatoes, broth and bay leaves, cover and place into the preheated oven for two hours.
After two hours add carrots and tomato paste and stir to combine. Cover and cook for 30 more minutes or until carrots are tender.
While the stew cooks for the last 30 minutes, in a medium sauce pan, melt butter and add flour over medium heat. Cook for five minutes stirring often with a wooden spoon. Remove from heat.
Once the stew comes out of the oven, turn the heat back on the butter and flour mixture and ladle in liquid from the stew and whip to make a thick sauce. Keep adding liquid until the mixture is no longer paste like. Transfer that back into the stew and gently stir to combine.