Because Cottage pie originates from a long time ago, it has been designed to tolerate and go well with the classic spices but you can experiment with not so classic as well.
Peel potatoes and cut into chunks. Place in a large pot of cold salted water.
Bring the potatoes to a gentle boil and cook 13-16 minutes or until fork tender.
While potatoes are cooking, combine ground beef and onion in a large skillet, brown until no pink remains.
Add carrots and garlic to the ground beef mixture. Cook for an additional 5 minutes or until slightly tender.
Stir in the flour and cook for 1 minute. Stir in beef broth, tomato paste, parsley, basil, rosemary, and bay leaf.
Simmer for 20 minutes or until the gravy has thickened. Remove bay leaf, add peas, and season with salt and pepper.
Drain the potatoes well and mash until smooth. Stir in the butter. Add warmed milk a little bit at a time until the potatoes are smooth and fluffy, you may not need all of the milk. Stir the cheese into the potatoes. Taste and season with salt and pepper.
Top the meat mixture with the potatoes and place in the oven. Bake 20-25 minutes or until golden.