British Baked Beans

Dried navy beans (rinsed)

salt (plus 1/2 teaspoon divided)

vegetable oil

large yellow onion (finely chopped)

small carrot (peeled and finely chopped)

stalk celery (finely chopped)

garlic (peeled and finely grated)

can crushed tomatoes

ketchup

granulated sugar

Worcestershire sauce