Preheat oven to 400°F and grease a large (2 quart) gratin or shallow casserole dish.

Cook bacon in a Dutch oven over medium heat until done but not too crisp; remove and drain on paper towels, reserving the fat in the pot.

Melt 1 tablespoon of butter in the reserved bacon fat; add sliced onion and cook until wilted, then transfer to a bowl.

Add cream, half-and-half, salt, and pepper to the hot pot and stir to combine.

Add sweet and russet potato slices to the pot, ensuring they are covered by the liquid (add more half-and-half if needed); bring to a simmer over medium-high heat, then reduce heat and simmer until the potatoes are tender but still firm, about 8 minutes.

Use a slotted spoon to separate the cooked sweet and russet potato slices into two bowls, allowing the cream mixture to continue steaming over very low heat.

Arrange half of the russet potato slices on the bottom of the greased baking dish. Spread 1/3 of the cooked onions and 1/3 of the bacon on top. Sprinkle 1/3 of the shredded Swiss cheese over everything, then ladle 1 cup of the steaming cream over the cheese.

Make a second layer using all of the sweet potato slices in place of the russet, layering with onions, bacon, and Swiss cheese as before, but without adding cream this time.

Top with a final layer using the remaining russet potato slices, onions, bacon, Swiss cheese, and finish with 1 cup of the cream. Allow the remaining cream to continue to steam very slowly, stirring occasionally, until reduced by half.

Place the gratin dish on a baking sheet to catch any spills, and bake for 30 minutes. Remove and set on a rack to rest for 10 minutes before serving.

While the au gratin is resting, stir the remaining 1 tablespoon of butter into the hot cream until blended, adjust seasoning to taste, and pour the sauce through a wire mesh strainer into a sauce boat.

Serve the gratin in its baking dish. Serve the reduced sauce on the side.