In a large bowl, combine garlic powder, coriander, fennel, paprika, 1 teaspoon salt, and 1/2 teaspoon pepper. Mix well.
Add pork and gently mix until seasonings are distributed evenly. Form into 6 patties approximately 1/2-inch thick each.
Preheat a large skillet or grill over medium-high heat. Add patties (frying in batches if necessary) and cook 3 to 5 minutes per side or until a thermometer inserted at the thickest part reaches 145 degrees.
While the burgers are cooking, in a small bowl combine feta cheese, mayonnaise, and mustard and mix well. Drain 2 to 3 pickled beet slices per person.
Transfer burgers to a plate and tent with foil to keep warm. Spread cut sides of buns with butter and toast in skillet or on grill until golden brown.
To assemble the burgers, spread the bottom of each toasted bun with some of the feta mustard. Top each with a pork burger and 2 to 3 pickled beet slices.
Adapted from Blue Apron recipe # 998, "Spiced Pork Burgers with Pickled Beets."