Grate the mature cheddar using the medium side of a box grater. Peel and finely grate the carrot, then gently squeeze out any excess moisture if it seems particularly wet. Finely slice the spring onions, keeping the pieces small so they distribute evenly throughout the filling.

Place the grated cheese, carrot, and sliced spring onions in a medium mixing bowl. Toss them together gently so the ingredients are evenly distributed. This combination creates the colorful appearance and satisfying crunch that make a traditional cheese savoury filling so appealing.

Add the mayonnaise, mustard, lemon juice if using, and black pepper to the bowl. Stir everything together until the cheese and vegetables are lightly coated. Begin with the recommended amount of mayonnaise and add a little more only if needed to achieve a creamy, spreadable consistency.

Taste the mixture and adjust the seasoning to your preference. Add a little more mustard for a sharper flavor, extra black pepper for warmth, or a small amount of lemon juice for brightness. Mature cheddar can be naturally salty, so taste before adding any extra salt.

Lay the bread slices on a clean work surface. Spread a thin layer of softened butter on the inside of each slice if desired, then divide the cheese savoury filling evenly between four slices. Spread it gently to the edges, add lettuce if you like, and cover with the remaining bread slices.

Press the sandwiches together gently and cut each one in half diagonally or into neat rectangles. Serve immediately for the freshest texture, with crisps, salad, or a bowl of soup on the side. If preparing them for later, wrap and refrigerate promptly to keep the filling fresh.