Turn the oven to 375, then prep all the ingredients. Scrub and peel your potatoes (if using red, fingerling or tiny taters, you can leave the skin on), and chop into 1-1.5" pieces. Break the broccoli into small florets and rinse well. Mince your garlic and grate the cheese. Chop the bacon (if using) and slice the shallots. Chop the butter into very small pieces (it helps if it's really cold) and then scatter all over the bottom of a baking dish (at least 8" x 5") or casserole.
Add the potatoes to a pot with some salted water (the level of the water should just cover the potatoes) and bring to a boil. Reduce heat and simmer for 7 minutes. Add the broccoli and simmer, covered, for an additional 2 minutes. Drain and discard the water.
While the potatoes and broccoli are cooking, add the bacon (or oil/butter if making vegetarian version) to skillet over medium high heat and cook for 5 minutes. Add the shallots and salt into the bacon and stir well, coating in the bacon grease, and cook till slightly softened (an additional 2-3 minutes.) Add in the garlic, cook for 1 more minute, and then turn off heat.
Pour the potatoes and broccoli into your prepared casserole/baking dish. Top with the shallot and bacon, and then the grated cheese.
Bake for 10-15 minutes in your hot oven*. Serve with greek yogurt or sour cream-- this is definitely essential, otherwise it might be a little dry.