Peel tomatoes by slicing a small X in the base of each tomato. Place tomatoes in a pot of boiling water for 30 to 45 seconds or until skin loosens. Remove tomatoes with a slotted spoon and slip skins off when cool enough to handle. Chop tomatoes.

To make tomato garlic jam, combine sugar and lime juice in a small saucepan. Warm over medium heat until sugar dissolves. Add chopped tomatoes, red bell pepper, garlic, and chili. Bring to a boil, reduce heat and simmer uncovered for 30 minutes or until mixture has reduced by about half. Stir in fish sauce (if using) and allow to cool to room temperature.

In a large bowl, gently mix together ground beef, shiitake mushrooms, cilantro, scallions, soy sauce, Chinese 5 spice, and ginger. Form into 4 equal-size patties.

Add a splash of olive oil to a non stick skillet over medium heat. Place patties in the pan. Cover and cook 4 minutes. Then flip and cook 3 to 4 more minutes. Serve burgers on buns topped with tomato garlic jam and shredded cabbage or coleslaw mix.