Cut poblano in half and remove seeds. Slice into slivers. Peel golden beet and grate it using a box grater.
Whisk 2 eggs until fluffy.
In a small nonstick omelet pan, add 1 teaspoon of butter over medium heat. Once melted, add shredded beets and poblano and cook for 3-4 minutes until they start to soften. Season with salt and pepper. Remove half of the mixture for the second omelet.
Spread beet mixture out over the surface of the pan and pour in eggs. Swirl eggs around to cover the whole pan. As eggs cook, use a flexible spatula to push eggs gently to the center and allow uncooked egg to flow to the outer edges of the pan.
Cook omelet until eggs are mostly cooked. Optionally, you can cover the pan for 30-45 seconds to really set up the eggs on top. A thin film of uncooked eggs on the surface is okay though in my book. You don’t need to flip the omelet at all.
When the egg is set to your liking, dot half of the pan with goat cheese. Use a heavy hand with it.
Once the goat cheese is on the eggs, carefully slide the omelet out of the pan and fold it over itself on your plate. The warmth from the eggs will gently melt the goat cheese.
Serve sprinkled with salt and pepper and a dash of hot sauce if you want. Repeat for second omelet.