Tomatoes: Preheat oven to 325 degrees. In a 9-inch pie plate, place tomatoes and garlic cloves. In a small bowl, whisk together olive oil, balsamic vinegar, thyme, light-brown sugar, and salt. Drizzle over tomatoes and garlic and bake in the oven until tomatoes are wilted and caramelized, 40 to 45 minutes. Set aside.
Frittata: Increase oven temperature to 425 degrees, with the rack in the upper third of the oven. Lightly beat eggs in a large bowl with a whisk. Season with salt and pepper; set aside.
In a 12-inch nonstick skillet, heat oil over medium-high heat. Add onions, season with salt and pepper, and cook, stirring, until tender, 12 to 15 minutes. Reduce heat to medium and add the stems of the chard; cook until tender, 3 minutes. Add the chard leaves and stir to combine. Cook until wilted, about 1 minute. Pour egg mixture into skillet. Cook, using a heatproof spatula to gently stir and push eggs from edges to center of pan so runny parts run underneath, until eggs begin to set, about 2 minutes.
Scatter cooked tomatoes on top of the frittata and evenly distribute feta cheese on top. Transfer frittata to oven and cook until top is set and has puffed slightly, about 15 minutes.
Gently run a spatula around the edges and underneath the frittata and carefully slide out of the pan onto a cutting board. Slice into wedges and serve hot, warm, or at room temperature.