Crack 2 large eggs and 1 large egg white into a small bowl. Add 1 teaspoon water and kosher salt and black pepper. Whisk until blended.
Heat 1/2 tablespoon olive oil in a medium nonstick skillet over medium heat until shimmering.
Add 1/4 cup onions to the skillet and cook, stirring occasionally, until tender and golden, about 3 to 4 minutes.
Add 1 1/2 cups thinly sliced mushrooms to the skillet and cook, stirring, until the mushrooms are tender and beginning to brown, about 3 to 4 minutes.
Add 1/2 cup fresh baby spinach and cook, stirring, until the spinach is wilted, about 30 seconds to 1 minute.
Reduce the heat to medium-low. Pour the whisked egg mixture evenly over the vegetables.
Let the eggs sit briefly until they begin to set at the edges, then gently stir and fold the mixture with a spatula until the eggs are thickened and no liquid egg remains, about 1 to 2 minutes. If using 2 tablespoons cheese, sprinkle it over the eggs as they start to set so it melts.
Remove the skillet from the heat, adjust seasoning with kosher salt and black pepper if desired, and serve immediately.