Place ¼ and ⅜ inch die, blade, screw and feeder shoot in freezer for at least an hour, preferably 3 hours. While grinder pieces are in freezer, make the buns.

In a glass measuring cup, combine ½ cup warm water, milk, yeast and sugar. Let stand until foamy, about 5 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, mix flours and salt on low until combined, about 30 seconds. Add the butter and mix on medium low until no visible butter remains, about 2 minutes. Replace paddle attachment with dough hook, then add egg and yeast mixture. Mix on low until all ingredients are combined, using a rubber spatula to scrape down the sides if needed, about 1 minute. Increase speed to medium, and knead for 8-10 minutes, until a ball of dough forms and clears the sides of the bowl. If dough does not clear sides of the bowl after 4-5 minutes, add bread flour, 1 tablespoon at a time, until it does. Scrape dough down into a ball, cover bowl with plastic wrap, and let rise in a warm place until doubled in size, 1 to 2 hours. While buns are rising, make candied bacon and burger sauce.

Preheat oven to 375°F. Line a baking sheet with foil and set aside.

In a small mixing bowl, add maple syrup and brown sugar and microwave for 30 seconds, or until sugar has dissolved.

Place bacon in a single layer on baking sheet and evenly brush the top of the bacon with half of maple brown sugar mixture. Bake for 8 minutes, then flip and brush other side with remaining maple brown sugar. Bake for an additional 6-8 minutes, then allow to cool slightly before transferring to a plate. Set aside.

In a small mixing bowl, add all ingredients and whisk to combine. Cover and refrigerate until ready to serve.

Line a baking sheet with parchment paper. Using a dough scraper, divide dough into 4 equal parts. Gently roll each into a ball and arrange 2 to 3 inches apart on baking sheet. Cover loosely with a clean kitchen towel and let buns rise in a warm place for 1 to 2 hours.

Set a large shallow pan of water on oven floor. Preheat oven to 400°F with rack in center. Brush top of buns with egg wash. Bake, turning sheet halfway through baking, until tops are golden brown, about 15 minutes. Transfer to a rack to cool completely.

Place meat on sheet tray and place in freezer for 30 minutes, or until meat is firm, but not frozen.

Fill a large bowl with ice and add a little bit of water. Insert a smaller bowl on top of the ice to catch the meat as it comes out of the grinder.

Reassemble grinder, using the ⅜-inch die and pass meat through grinder, being sure not to overpack the feeding tube/loading tray.

Line a sheet tray with parchment paper and place underneath meat grinder. Change die to ¼-inch and pass meat through again, using care to not squish the meat when adding it to the feeding tube/loading tray.

Equally divide meat into four 6-ounce patties and refrigerate on sheet tray until ready to cook.

In a large cast iron skillet over medium high heat, add oil. Season patties assertively with salt and once oil is shimmering, add 2-3 burger patties to the skillet. For medium burgers, cook for 2-3 minutes, or until deeply golden brown, then flip and repeat on other side. Top with cheese, remove from the heat and cover with lid. Allow cheese to melt, then transfer to a plate. Repeat until all burgers are cooked.

Add a generous amount of burger sauce to the top and bottom bun. Add arugula, cheeseburger, candied bacon, tomato and red onion. Serve immediately.