Pour beetroot, 100 g cheese and honey into a tall mixing bowl and puree finely. Season to taste with salt and pepper. Crumble the remaining cheese and fold in. Wash cucumber, grate dry and cut into thin slices. Wash chives, shake dry and cut into fine rolls.
Whisk eggs with milk and season with salt. Heat oil with butter in a large coated pan and fry whisked eggs until scrambled. Spread breads with beetroot cream, spread scrambled eggs on top, garnish with cucumber slices and chives. Sprinkle with pepper.