Ingredients

1/2 cup chopped onion, divided

1 tablespoon olive oil plus additional for brushing

1/2 cup bulgur

1 cup water

1 cup canned pinto beans, rinsed and drained

1 1/2 tablespoons soy sauce

3/4 cup walnuts (2 1/2 oz)

2 garlic cloves, coarsely chopped

1/2 cup packed cilantro sprigs

3/4 teaspoon ground cumin

1/4 teaspoon cayenne

1/4 cup mayonnaise

1/4 teaspoon grated lime zest

1/2 teaspoon fresh lime juice

4 slices multi-grain bread, toasted

Preparation

Equipment: a perforated grill sheet * Accompaniments: lettuce; sliced tomato

*

  Cook half of onion with 1/4 tsp salt in oil in a small heavy saucepan over medium heat, stirring occasionally, until golden, 5 to 7 minutes. Add bulgur and water and cook, covered, over low heat until water is absorbed, 15 to 18 minutes. Transfer to a bowl and stir in beans and soy sauce.

*

  Pulse bulgur mixture, walnuts, garlic, cilantro, cumin, cayenne, a rounded 1/4 tsp salt, 1/2 tsp pepper, and remaining onion in a food processor until finely chopped.

*

  Form rounded 1/2 cups of mixture into 4 (31/2-inch-diameter) patties. Chill at least 10 minutes.

*

  While patties chill, stir together mayonnaise, zest, and juice.

*

  Prepare grill for direct-heat cooking over medium-hot charcoal (medium heat for gas); see "Grilling Procedure." Put perforated grill sheet on grill and preheat 10 minutes.

*

  Brush patties all over with oil.

*

  Oil grill sheet, then grill burgers on grill sheet, covered only if using a gas grill, carefully turning once, until golden brown, about 8 minutes total.

*

  Serve burgers open-faced on toast with lime mayonnaise.

Cooks’ notes:

* Burgers can be cooked on the stove. Heat 1 Tbsp oil in a 12-inch heavy skillet over medium heat until it shimmers, then cook patties, carefully turning once, until golden brown, about 8 minutes total.

* Uncooked patties can be chilled, covered, up to 4 hours.