Position racks in the upper and lower thirds of the oven; preheat to 450 degrees F. Whisk the eggs, mustard, garlic, thyme, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Add the chicken and toss. Let sit 10 minutes.
Toss the broccoli, tomatoes, olive oil, 1/2 teaspoon salt and a few grinds of pepper on a rimmed baking sheet. Roast on the upper oven rack until the broccoli is tender and browned and the tomatoes burst, about 25 minutes.
Meanwhile, whisk the panko, cornstarch and 1/2 teaspoon salt in a shallow bowl. Remove the chicken from the marinade, letting the excess drip off, and dip in the panko mixture to coat completely.
Heat about 1/4 inch of olive oil in a large ovenproof skillet over medium-high heat. Add the chicken and cook until golden brown, about 4 minutes per side. Transfer the skillet to the bottom oven rack; bake until the chicken is cooked through, about 2 minutes. Serve with the vegetables and rice. Photograph by Antonis Achilleos
Kids' Meal: Teach kids how to strip thyme sprigs: Pull down along the stem in the opposite direction of the leaves-they'll fall right off!