Bring a medium saucepan of water to a boil. Add the quinoa, and cook until tender, 10 to 12 minutes. Strain well, and cool completely. (The quinoa can be cooked a day ahead.)
Put the vinegar, 1 tablespoon of the oil, mustard, 1 tablespoon water, 1/4 teaspoon salt and a few grinds of pepper in a jar or other container with a lid. Secure the lid, and shake until combined. (The vinaigrette can be made a day ahead; shake well before serving.)
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat. Add the peppers and onions, and cook, stirring occasionally, until they are just tender and browned in some spots, 5 to 7 minutes. Add the hot sauce, and stir. Remove the skillet from the heat, and let the vegetables cool completely. Wipe out the skillet, and set aside.
Toss the quinoa, pepper-onion mixture, spinach, ham, Cheddar and scallions with the vinaigrette in a large bowl. Season to taste with salt and pepper. Divide among 4 serving bowls.
Heat the remaining 1 tablespoon oil in the skillet over medium heat. Pour in the eggs, and add a pinch of salt. Tilt the skillet so the eggs completely cover the bottom. As the eggs turn from runny to cooked at the edge of the skillet, push the cooked eggs all around the edge to the middle of the skillet with a heatproof spatula so the uncooked eggs can spill into the free space and cook (this helps the eggs cook faster, and you won't have to flip the omelet). Once all the eggs are just cooked through, slide the omelet out onto a cutting board. Let it cool for a few minutes, then roll it up into a cylinder and cut it into 1/2-inch slices. Top each salad with a few "pinwheels" of egg. Serve hot sauce on the side.
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