1 1⁄4 pounds ground beef
1 large red onion, cut crosswise into 4 thick slices
2 tablespoons grated fresh ginger
1 tablespoon Asian-style mustard (Chinese hot mustard)
2 garlic cloves, minced
2 tablespoons teriyaki sauce
2 cups broccoli slaw
1 teaspoon rice vinegar
4 hamburger buns
1⁄2 teaspoon salt
4-ounce log chevre (soft goat cheese)
1⁄4 teaspoon ground black pepper
In a large bowl, combine the beef, ginger, garlic, teriyaki sauce, vinegar, salt, and pepper. Use your hands to blend the ingredients, then shape the mixture into 4 patties.
When the grill is hot, lightly oil the grates. Grill the burgers for 6 to 7 minutes per side, or until desired doneness. Grill the onions for about 4 minutes per side, or until soft.
Meanwhile, in a medium bowl, mix together the mustard and mayonnaise. Add the broccoli slaw and toss well. Divide the mixture among the bottom halves of the buns.
When the burgers are done, place each on top of a coleslaw-covered bun, then use a butter knife to spread a quarter of the goat cheese onto the burger. Top with an onion slice and bun.