Place mushrooms in a small bowl; cover with boiling water.
Let soak for 10 minutes.
Drain, rinse well, and chop.
Combine chopped porcini mushrooms, ground beef, basil, thyme, garlic, salt, and pepper in a large bowl.
Shape into 6 patties about 3/4-inch thick.
Brush patties with olive oil.
Place burger patties on the lightly oiled rack of an uncovered grill directly over medium heat.
Grill for 14 to 18 minutes, turning burgers once halfway through grilling.
Place focaccia wedges on the grill rack; grill for 1 to 2 minutes or until toasted.
Remove burgers and focaccia from grill.
Place each burger on a wedge of focaccia; sprinkle immediately with cheese.
Spoon Tomato Relish on top.
Makes 6 burgers.
Or use hamburger buns and grill.
Tomato Relish: In a medium mixing bowl stir together 1/2 of a medium yellow tomato, chopped, 1/2 of a medium red tomato, chopped; 1 cup cut-up cherry tomatoes, 1/4 cup finely chopped sweet onion, 1 tbls.