Warm the olive oil in a medium skillet over medium-high heat. Add the onions and cook until starting to soften, 2 to 3 minutes. Add the yellow squash and zucchini, sprinkle with salt and pepper and stir and cook for 3 to 4 minutes. Remove from the heat and set aside.
Grill the tomato slices on a grill pan or simply sear them in a hot skillet. Remove and set aside.
Bring a medium saucepan of water to a gentle boil. Add the vinegar. Use a wooden spoon to carefully stir the water into a circular "whirlpool." Crack the eggs into the water and allow them to swirl around in the water until they begin to set. Let them stay in the water for 1 minute, then remove them with a slotted spoon and set on a plate. If the eggs need to be cooked longer, just add them back to the water for 30 seconds at a time.
Spoon the vegetables on a plate or in a bowl and set the eggs on top. Lay the tomato slices on the side. Place the cheese slice on the side. Sprinkle the eggs with salt and pepper and serve!