Scale your milk and eggs into the bowl of your stand mixer, and reserve that bowl in the fridge until ready to mix. Scale flour, salt, and yeast together in a separate bowl. Scale beef tallow, and keep chilled. Scale white sugar separately.
Set up your electric stand mixer for bread mixing: dough hook for a Kitchenaid and dough roller & scraper attachments for an Ankarsrum. Place your flour, salt, and yeast on top of the chilled milk and eggs, and mix for 5 minutes on a low speed, until a homogenous mass of dough is made.
Then, mix on slightly faster medium speed for 5 more minutes.
After that 5 minutes, begin adding your beef tallow and sugar, alternately, starting with a third of the chilled beef tallow. Once that has fully incorporated, follow up with half of the sugar, and continue to mix in this manner until all the butter and sugar has been incorporated. Each addition must be fully incorporated before the next addition.
If your dough starts to break or look overly greasy, have patience, and continue mixing at a higher speed to emulsify the fat and sugar into the dough. The final dough should have a homogenous texture and it should ball up when being mixed. This can take up to another 5-10 minutes of mixing to achieve.
On a parchment-lined sheet pan, take the dough and press it into the pan to about a 1-inch thickness, cover, and place in the fridge to firm up before scaling and shaping.
To scale/shape/proof the dough:
About 4-6 hours before you would like to bake, take the chilled dough and using a scale, weigh out the dough into 115-gram portions. Round out the portions into balls, and flatten the rounds slightly into 3/4" discs.
Space 6 brioche discs evenly onto an 18"x 13" sheet pan, lined with parchment paper. Cover the sheet pan in plastic (reference the video to do this effectively).
Allow the dough to rise at room temperature for 4-6 hours, depending on your environment. Once doubled in size, or roughly 4 inches in diameter, you are ready to bake.
To finish/bake the brioche:
Preheat your Yoder Smokers Pellet Grill to 325-350°F, with the diffuser plate in place, using the pellet flavor of your choice.
Create your egg wash by whisking together one egg with a pinch of salt and about a teaspoon of water until totally smooth with no lumps of egg present.
Remove the plastic wrap and brush the entire surface of the burger buns with egg wash and follow up with a heavy sprinkling of Cattleman's Grill Everything Bagel Seasoning.
Bake centered on the top rack of the pellet grill for 25-35 minutes, rotating about halfway through the cook. The surface should have a golden brown color, with a minimum internal temperature of 190°F.
Cool completely before removing from the pan and slicing for burger buns.
**Recipe Notes: To make slider-sized buns, scale 45 gram portions. For buns that are more conventionally-sized buns, scale 85-gram portion.