Trim the stem ends of the green beans.
Place a steamer basket in a large pot filled with a few inches of water. Add the green beans to the basket. Bring to a boil and cover. Cook until green beans are crisp but tender, about 5 to 7 minutes.
Melt the butter in a saucepan. Add the sage leaves. Continue to cook the butter until it is nut brown and very fragrant, about 8 to 12 minutes. Scrape solids off the bottom of the pan with a spatula. Reserve fried sage leaves for garnish.
Place egg yolks into a blender and add lemon juice, cayenne, mustard and season well. Pulse once or twice. Pour hot brown butter into the blender slowly in a thin stream to emulsify.
Keep sauce warm and pour over the beans, garnishing with the fried sage leaves.