Put peaches, sliced onions, vinegar, 2 tablespoons water, 1 tablespoon of the mustard, sugar, 1/4 teaspoon of the salt and 1/4 teaspoon pepper into a small pot and bring just to a boil over medium-high heat.

Reduce heat to medium low and simmer, stirring occasionally, until liquid is thickened and peaches are very tender and just starting to fall apart, 5 to 7 minutes.

Transfer peaches to a bowl and set aside to let cool. (If there seems to be too much liquid, drain if needed.)

Prepare a grill for medium-high heat cooking, oiling the grill grates if necessary.

In a large bowl, combine pork, chopped onions, parsley and remaining 1 tablespoon mustard.

Form the mixture into 4 patties.

Brush patties all over with oil then season with remaining salt and pepper.

Grill burgers, flipping once, until deep golden brown and cooked through, about 10 minutes total.

Divide spinach between pita halves then tuck one burger into each half.

Spoon pickled peaches into pitas and serve.