Heat the olive oil and butter in a large skillet over medium high heat.
Add the onions and saute until they start to soften and change color, about 10 minutes.
Reduce the heat to low and let them cook until they turn a gorgeous golden brown and smell incredibly sweet, another 30 minutes or so, stirring every 15 minutes or so. If the onions start to dry out, turn the heat down some more and add a little more olive oil.
Add the thyme and brandy and stir to combine. Season with salt and pepper. Cook for 10 minutes more.
Preheat the oven to 350°
Pull the dough out of the fridge and let it come to room temperature while the onions are finishing. Now's a good time to grate the cheese if you haven't already.
Roll the dough out, using a little flour to prevent sticking.
Transfer to a baking sheet. It's OK is it extends past the edges.
Spread 2/3 of the cheese on the dough, leaving an inch or more all the way around.
Arrange the onions over top the cheese. Fold the sides up, leaving some of the onions exposed in the middle.
Spread the remaining cheese on top.
Bake for 30 - 35 minutes. The top will turn a nice golden brown.