Sprinkle the rabbit legs with salt and pepper. Place a large Dutch oven over high heat and add the oil. Let get hot, then add the rabbit legs and sear on both sides, 5 to 7 minutes per side. Transfer to a plate until ready to use.
Reduce the heat to medium-low, then add the onions. Season with salt and saute until translucent, 5 to 7 minutes. Add the vermouth and mustard and bring to a simmer. Add the butter, the rabbit legs and rosemary atop the onions. Cover the pan and bake until the rabbit is tender, 35 to 40 minutes.
Remove the rabbit from the Dutch oven and set aside. Put the Dutch oven back over medium-high heat and add the cream to the cooking liquid and onions. Cook until heated through and thickened, about 2 minutes.
For the spaetzle: Bring a large pot of water to a boil.
Whisk the eggs, milk, rosemary, salt and pepper together in a small mixing bowl. Add the flour gradually until a thick batter is formed.
Over the boiling water, push the batter through the bottom of a colander with a spatula and simmer until the spaetzle float to the top, 3 to 4 minutes. Strain and place on a paper towel-lined sheet tray. Let cool slightly.
Heat a 14-inch cast-iron pan over medium-high heat. Add the butter and heat until frothy and browned. Add the spaetzle and cook until crisp, 2 to 3 minutes. Drain on the paper towels and season with salt.
Place the spaetzle in a large shallow dish and top with the rabbit legs. Pour the sauce over the legs and serve.
Copyright 2021 Television Food Network, G.P. All rights reserved.