In a large skillet or Dutch oven, cook the ground beef over medium-high heat, breaking it up with a wooden spoon, until browned and any excess moisture has evaporated, about 5-7 minutes.
Reduce the heat to medium and add the diced onion and minced garlic. Cook, stirring frequently, until the onions are translucent and the garlic is fragrant, about 3-5 minutes.
Stir in the Worcestershire sauce, tomato paste, thyme, paprika, cumin, and red pepper flakes (if using). Let the mixture simmer for 2-3 minutes to allow the flavors to meld.
Sprinkle the flour over the beef mixture and stir to coat. Cook for 1 minute, then gradually pour in the beef or chicken stock, stirring constantly to prevent lumps from forming.
Bring the mixture to a gentle simmer and let it cook, stirring occasionally, until the sauce has thickened to your desired consistency, about 10-15 minutes.
Season the savory mince with salt and pepper to taste.
Serve the savory mince hot, either on its own or with your choice of accompaniments, such as mashed potatoes, rice, or steamed vegetables.