Heat the oil in a large skillet over medium-high heat. Just before it starts to smoke, add the tomatoes (they will pop and sputter). Cook until the tomatoes blister and their skins char, 3 to 4 minutes. Reduce the heat to medium-low, add the garlic, and cook for 1 minute. Turn off the heat and add the feta. Add the oregano and cayenne, and season with salt and pepper. Stir in the broth and serve.
If you can't find French feta, you can substitute Greek feta. Just use a little less (about 3 ounces), because Greek has a stronger flavor.