Preheat oven to 190 C / Gas 5. Place squash in a baking dish and pour in enough boiling water to come 1.25cm (1/2 inch) up the sides of the dish.
Bake in the preheated oven until squash is tender, 40 to 45 minutes. Remove from oven; cool until easily handled, 7 to 10 minutes.
Reduce oven to 180 C / Gas 4. Scoop out the flesh of the squash and separate strands with a fork. Reserve shells.
Cook beef, onion and pepper in a frying pan over medium heat until the beef is browned, about 5 minutes. Stir in garlic, basil, oregano, salt and pepper; cook and stir until fragrant, about 2 minutes. Add tomatoes and cook until warmed through, about 2 minutes. Stir in squash; cook until liquid has evaporated, about 10 minutes.
Fill squash shells with squash mixture using a slotted spoon. Place in a shallow baking dish.
Bake in the preheated oven until flavours combine, about 15 minutes. Sprinkle with Cheddar cheese and continue to bake until cheese is melted, about 5 minutes.
Any mince can be substituted for beef mince. You can also use mozzarella cheese instead of Cheddar.