Preheat the oven to 225 degreesF. Combine the flour, half the thyme, salt and pepper in a shallow bowl. Place the eggs in a second shallow bowl. Add the chicken breasts and turn to thoroughly coat with egg. Heat 2 Tbsp. of the oil in large, non-stick skillet set over medium-high. Coat the chicken breasts in the flour mixture; pan-fry 3 to 4 minutes per side. Transfer to a heatproof plate and keep warm in the oven. Add the remaining oil to the skillet and lower the heat to medium. Add the onions, garlic and remaining thyme and cook, stirring, until the onions are translucent, about 5 minutes. Increase the heat to medium-high and cook until the onions are golden brown, about 5 minutes more. Add the wine to the skillet and cook one minute. Add the stock, tomato paste and sugar, bring to a boil, and cook 2 minutes more. Return the chicken to the pan and heat through, about 3 to 4 minutes, turning once and then serve.