In a large bowl, combine all Elk Burger ingredients. Gently mix until just combined – do not overmix.
Form the mixture into 4 patties.
Prepare the Hatch Chile & Smoked Gouda Jam: In a saucepan, melt brown butter over medium heat. Add shallots and cook until softened. Add red wine vinegar and reduce by half. Stir in Hatch chiles and smoked Gouda until melted and combined. Set aside.
Preheat grill to medium-high heat.
Grill the elk burgers for 4-6 minutes per side, or until cooked to desired doneness (internal temperature of 160°F/71°C).
Toast the pretzel buns lightly.
Assemble the burgers: Spread Hatch Chile & Smoked Gouda Jam generously on both buns. Top with the elk burger and microgreens. Finish with the top bun.