Heat oil over medium heat in a large frying pan and saute garlic for a few seconds until fragrant. Add chopped carrots and onion and saute until onions are translucent. Add chopped chicken and cook through. Salt to taste (we're adding ketchup next, so not too salty) and stir in rice. Stir in ketchup.
Take 1/3 of the chicken rice and place on a plate. Use a damp paper towel to shape rice into a football shape. Repeat with remaining rice, to make three footballs.
Heat a large non-stick skillet over medium heat. Whisk eggs, salt, and milk. Pour one egg's worth into the skillet and swirl pan to evenly distribute. Cook through and set aside on a plate. Repeat two more times. Add the remaining 3 eggs worth and scramble until set, but not cooked through. Add 1/3 of the scrambled egg on top of each rice football. Place the thin cooked-egg "skin" over each football, and using another damp paper towel, fix the shape and tuck in the along the sides.