Whisk together all ingredients. Transfer to a squeeze bottle or bowl in the fridge until ready to use.
For the nachos
Preheat oven to 425 F.
Prepare the tater tots or crispy crowns accoring to package instructions. Make sure to get them good and crispy. Season well with salt and pepper. Reduce the oven temperature to 300 F for melting the cheese before serving.
Add half the oil to a large skillet or saute pan over high heat. Add the ham and cook until just starting to brown on the edges. Transfer to a paper towel-lined plate.
Add the remaining oil. Add the mushrooms, peppers and onion. Stir and cook until the vegetables are just starting to turn tender. Transfer to a bowl. Add in the ham. Stir and season with salt and pepper.
Whisk together the eggs and milk in a small bowl. Season with salt and pepper.
Add the butter to the skillet and reduce heat to medium. Add the eggs. Stirring constantly, scramble the eggs until just set (do not overcook!). Remove to a plate and lightly break up the eggs using a fork.
Assemble the nachos by dividing the tots between 4 oven-proof plates. Top with the ham and vegetable mixture, followed by the eggs.
Sprinkle with cheese and place in the oven for about 3 minutes or until the cheese has melted.
Serve drizzled with the sauce and garnished with the green onions.