Heat a large skillet over medium, medium-high heat. In a bowl, toss together the red onion, shallot, and 2 tablespoons of olive oil until thoroughly coated.

Dump the contents of the bowl into the heated skillet and saute until the onions and shallot just begin to soften and turn translucent, around 3 minutes.

In the same bowl, toss together the tomatoes and remaining olive oil, then turn over into the skillet with the onion and shallot. Sprinkle with salt and pepper and allow to cook, stirring occasionally, until the tomato skins blister and soften, around 5 minutes.

Add the fresh basil at the last minute, stir gently, then remove from heat, sprinkle with the feta cheese, and serve immediately.