Heat the oil in a large skillet over medium-high heat. Cook the beef, onion and carrot for 7 to 8 minutes, breaking up the beef and cooking it to 160°F.
Stir in tomato paste and flour for 1 minute. Gradually stir in broth, then add Worcestershire, thyme, salt and pepper.
Simmer over medium heat for 6 to 8 minutes, stirring occasionally, until the carrots are tender and the gravy coats the beef.
Add the frozen peas and cook for 2 minutes until hot. Toast the bread while the gravy finishes, then spread with butter.
Put two toast slices on each plate and spoon the mince over them just before serving.