Combine the feta and 3 tablespoons of olive oil in a food processor, and process until completely smooth, about 2 minutes. In a medium bowl, combine the lamb, herbs, garlic, salt, and 1 tablespoon of olive oil. Mix well. Form the mixture into 4 patties. Grill the patties over high heat until cooked through, about 2-3 minutes per side. Remove the burgers from the grill and set aside. While the burgers rest, brush the tomatoes with the remaining olive oil, and place on the grill.
