Preheat the oven to 350˚F. Smear ½ tablespoon butter all over the inside of a 9" X 13" baking dish. Set aside.
Melt the remaining butter in a medium pot over medium heat. Add the sliced shallot and garlic and sauté for 5 minutes.
Stir in the cream and milk. Add the bouillion, mustard, salt, pepper and thyme sprigs. Simmer for 15 - 20 minutes, until reduced by ¼ cup. Let cool and remove the thyme.
Roast the poblano pepper on a baking sheet under a broiler until the skin blisters, turning as needed. This should take about 15 minutes. Place in a jar or plastic bag. Seal and wait for 10 minutes. Remove the pepper and peel. Slice open, scrape out the seeds, and dice.
Thinly slice the potatoes, approximately ⅛" thick. I use a hand-held mandolin, and set it on #2 setting.
Arrange the potato slices like shingles on the bottom of the baking dish until the bottom is covered. Lightly salt and pepper the potatoes, and sprinkle ⅓ of the Gruyere cheese and ⅓ of the diced poblanos over the slices.
Repeat for 2 more layers, finishing with the final ⅓ of the Gruyere and poblanos. Pour the cream reduction over the potatoes. Cover the baking dish tightly with foil. Bake for 60 - 75 minutes, until the potatoes are tender. If baking this at 5000-7000 feet, you may need to bake it for 75 - 85 minutes.
Uncover, sprinkle with Parmesan and toasted breadcrumbs, if using. Bake for an additional 10 minutes.
Serve piping hot.