Thinly slice the onion and add to a pot over medium heat with the butter, olive oil, and brown sugar. Cook until the onions start to soften, then add ¼ cup beer.

Cook, stirring occasionally over medium heat until onions have turned dark brown and the beer has evaporated, about 45 minutes. Add the additional beer and cook until the pan is mostly dry with only about a tablespoon of liquid left (can be made 2 days in advance, store in the fridge in an air tight container).

Trim the rind off the brie, cut into small cubes. In a small bowl stir together the thyme, chives, brie, mascarpone and cornstarch.

Add the onions in an even layer to the bottom of an oven safe baking dish, top with cheese in an even layer.

Bake at 375 for 15 minutes or until the cheese is bubbly, stir to combine. Serve warm with baguette slices.