Heat 1 teaspoon olive oil in a large nonstick skillet set over medium heat. Add the carrots and saute until starting to soften, about 3 minutes. Pour in an additional teaspoon of olive oil. Add the onion, thyme and oregano and saute until the onions are tender, 4 to 5 minutes. Add the garlic and saute for an additional 30 seconds. Transfer the mixture to a bowl.
Turn the heat to medium-high. Lightly coat the skillet with cooking spray, then add the ground turkey. Season with salt, pepper and crushed red pepper flakes. Cook, breaking up the turkey with a wooden spoon, until the turkey is cooked through. Drain any liquid.
Return the vegetable mixture to the skillet, along with the cauliflower rice. Stir in the tomato sauce, barbecue sauce, tomato paste, Worcestershire sauce and honey.
Bring to a boil, then simmer until the cauliflower rice is tender, stirring occasionally, 5 to 6 minutes.