Sauté the Aromatics: Heat the olive oil in a large, heavy-based frying pan or Dutch oven over a medium heat. Add the finely chopped onion and cook for 5-7 minutes, stirring occasionally, until it has softened and become translucent.

Brown the Beef: Add the beef mince to the pan. Break it up with a wooden spoon and cook until it's browned all over. This step is crucial for developing flavour, so don't rush it. You can learn more about the importance of the Maillard reaction in browning meat from sites like Serious Eats. Once browned, drain off any excess fat from the pan.

Add the Garlic: Stir in the minced garlic and cook for another minute until fragrant. What works best for me is to make a little well in the centre of the meat so the garlic cooks directly on the pan's surface, which helps release its aroma.

Create the Sauce: Pour in the tomato ketchup, water, brown sugar, apple cider vinegar, English mustard, Worcestershire sauce, and smoked paprika. Stir everything together until the beef is evenly coated.

Simmer to Perfection: Bring the mixture to a gentle boil, then reduce the heat to low. Let it simmer, uncovered, for 20 minutes, stirring every few minutes to prevent it from sticking. The sauce will thicken and the colour will deepen.

Season and Rest: After 20 minutes, taste the mixture and season with salt and black pepper as needed. Remove from the heat and let it rest for 5 minutes while you prepare the buns.

Assemble the Sandwiches: Slice your buns in half and lightly toast them. Spoon a generous amount of the beef mixture onto the bottom half of each bun. If using, sprinkle a good handful of grated cheddar over the hot meat so it gets gloriously melty. Place the top half of the bun on and serve immediately.