Put a rimmed baking sheet on the lowest oven rack and preheat to 425 degrees F. Bring a large pot of salted water to a boil.
Toss the carrots with the olive oil; season with 1/4 teaspoon salt and a few grinds of pepper. Spread the carrots and sausages on the hot baking sheet and roast, tossing halfway through, until the carrots are tender and the sausages are browned, about 15 minutes.
Meanwhile, whisk the flour, eggs, milk and 1/2 teaspoon salt in a large bowl until smooth. Set a large-holed metal colander over the pot of boiling water (the colander should not touch the water). Add the batter to the colander and scrape with a rubber spatula, allowing small pieces to fall into the water. Simmer until the spaetzle floats to the top and is cooked through, 2 to 3 minutes. Drain and shake off the excess liquid.
Melt the butter with the mustard, 1/4 teaspoon salt, a pinch of pepper and the nutmeg in a large skillet over medium-high heat. Add the spaetzle and cook, tossing, until lightly browned and crisp, about 2 minutes. Add the dill and toss to coat. Serve the sausages and carrots with the spaetzle.