Mix mayo, shredded Pepper Jack, hot sauce, and pimentos in a small bowl. Set aside.
In a medium bowl, whisk together eggs, milk, and salt and pepper.
In a medium nonstick skillet, melt butter over medium heat.
Pour eggs in and cook, without stirring, until edges are set.
Use a spatula to gently flip the omelet over and spread the pimento cheese filling over the eggs. Fold the omelet over to cover the filling and slide onto a serving plate.
Top with diced chives and additional shredded cheese and serve warm.