The Ooh-La-La Burger

This is fantastic, anytime you add sauteed onions and mushrooms to a hamburger you make magic.  But add some red wine to the onions and ooh-la-la!  The French Bread is fun...but experiment with what you like.  I would stay away from an Onion Bun though - I think it would overpower the onions and mushrooms.

RED WINE CARMELIZED ONIONS
1 tbsp olive oil
1 sweet onion, thinly sliced
1/4 tsp each kosher salt and black pepper
1/4 cup red wine
1 tbsp packed brown sugar

SAUTEED MUSHROOMS
2 tbsp olive
250 g button mushrooms, thinly sliced
1/4 tsp each kosher salt and black pepper
1 clove garlic, minced
1/2 tsp finely chopped fresh thyme

BURGERS
750g medium ground beef (I used lean)
1/4 cup finely chopped shallot
3 tbsp finely chopped fresh tarragon
2 tbsp grainy Dijon mustard
2 cloves garlic, minced
1/2 tsp each kosher salt and black pepper
125 g brie cheese, thinly sliced
8 slices French Bread (not baguette)
Grainy Dijon mustard to taste
2 cups lightly packed washed and dried mache (lambs lettuce) (or baby spinach if you prefer)