In the bowl of a heavy duty mixer, combine milk, yeast, 1 egg and 1 cup of flour. Mix the ingredients together with a rubber spatula, until everything is blended. This is called the sponge. Sprinkle over the remaining cup of flour to cover the sponge. Set sponge aside to rest for 30 to 40 minutes.
After this resting time, the flour coating will crack. When this happens, add the sugar, salt, additional eggs and 1 cup of the flour to sponge.
Set in the mixer, attach the dough hook and mix on low speed for a minute or two, just until the ingredients look as if they are about to come together. Then, still mixing on low, sprinkle in 1/2 cup more flour.
When flour is incorporated, increase the mixer speed to medium and beat for 15 minutes, stopping to scrape down the hook and bowl as needed. During this mixing period, the dough should come together and wrap itself around the hook and slap the side of the bowl.
With the mixer on medium speed, add the butter a few tablespoons at a time.
When all the butter has been added, raise the mixer to medium-high for a minute, then reduce the speed to medium and beat the dough for about 5 minutes, or until you once again hear the dough slapping against the sides of the bowl.
If it looks as though the dough is not coming together after 2-3 minutes, add up to 1 tbsp more flour. It will be soft and still sticky and may cling slightly to the side and bottom of the bowl.
FIRST RISE: Transfer the dough to a very large buttered bowl, cover tightly with plastic wrap, and let rise at room temperature until it doubles in bulk, 2 to 2-1/2 hours.
SECOND RISE AND CHILL: Deflate the dough by placing your fingers under it, lifting a section of the dough, and letting it fall back into the bowl. Work your way around the dough, lifting and releasing.
Cover the bowl tightly with plastic wrap and refrigerate the dough overnight, or for at least 4 to 6 hours. Dough is ready to use.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 400 degrees F and preheat, lid closed, for 10 to 15 minutes.
Season salmon with salt and black pepper. Place salmon on the grill until it reaches an internal temperature of 90 degrees F, a little over halfway cooked. Reserve.
On the stovetop, heat 2 cups of water, 1 tsp olive oil and 1 smashed garlic clove. When water is boiling, add 1 cup quinoa, cover pan with lid and turn off stove. Let rest.
In a frying pan add 2 tsp unsalted butter, 1 tsp of ginger and 1 tsp mushrooms. Saute mushrooms, add 1/2 cup white wine and cook until most liquid has evaporated. Sprinkle on top lemon zest and chives. Reserve.
On a dry and floured surface, roll 1/2 of the brioche dough with a rolling pin (large enough to fit the piece of salmon).
Place dough on a baking sheet. In the center of the dough arrange a even layer of quinoa. Next lay the salmon and the mushrooms on top of the salmon. Roll out the other half brioche dough, place it on top of the salmon and close all around by folding the two pieces of dough together, like a pie.
Mix an egg with 1/4 cup water and brush this egg wash all over the top of the dough.
To finish, place the sheet pan in the Traeger and bake at 400 degrees F for 50 minutes, or until the dough is deep golden brown and crisp.
Slice and serve. Enjoy!