Crack the 3 large eggs into a medium bowl. Add 2 tablespoons milk, 1 teaspoon salt, and 1/4 teaspoon black pepper. Whisk vigorously until the mixture is homogeneous and slightly frothy (about 20–30 seconds). Set aside.

Vegetables

Prepare vegetables

Finely dice the yellow onion and red bell pepper so you have about 1/4 cup of each. Clean and slice mushrooms to measure 1/2 cup. Halve cherry tomatoes and roughly chop spinach if large.

Sauté vegetables

Heat a 10-inch nonstick skillet over medium heat. Add 1 teaspoon olive oil and 1 tablespoon butter. When the butter melts and begins to foam, add the diced onion and bell pepper. Sauté for 2–3 minutes until softened. Add the sliced mushrooms and continue cooking 2–3 minutes until mushrooms release moisture and begin to brown. Add the spinach and cherry tomatoes and cook 30–60 seconds until spinach wilts and tomatoes warm through. Spread the vegetables evenly across the pan and reduce heat to medium-low.

Egg assembly & cooking

Give the egg mixture a quick re-whisk and pour it evenly over the sautéed vegetables in the skillet. Tilt the pan so eggs cover vegetables in a thin layer.

Let the eggs set gently: without stirring, allow the omelette to cook for 1–2 minutes until the edges begin to set. Using a rubber spatula, lift the edges and tilt the pan to let uncooked egg flow underneath. Continue until the top is mostly set but still slightly glossy (another 1–2 minutes).

Sprinkle 1/4 cup grated cheddar cheese across one half of the omelette and scatter 1 tablespoon chopped chives over the cheese.

Fold the omelette in half using the spatula to cover the cheese. Cook an additional 30–60 seconds to melt the cheese and finish cooking; if you prefer more browning, increase heat to medium for the last 15–20 seconds, watching carefully to avoid burning.

Finish & serve

Slide the omelette onto a plate. Taste and adjust seasoning with a pinch of salt and pepper if desired. Serve immediately while hot.