Preheat the oven to 400 degrees. Scrub the carrots well (no need to peel them), and trim off the ends if desired. Rub each carrot with a little coconut oil and place them on a rimmed baking sheet. Season with salt and roast until carrots are tender and blistered, 20 to 30 minutes.
Meanwhile, make the dressing: in a small skillet, melt the butter over medium heat. Continue to heat until the butter has changed color from yellow to light brown, 5 to 7 minutes. The butter can burn very quickly, so keep an eye on it. Add the minced garlic and remove from the heat.
Pour the butter and garlic mixture into a jar with the mustard, vinegar, and a generous pinch of salt. Seal the jar and shake vigorously to blend.
Remove the carrots from the oven and place them on a platter. Pour the dressing over top and scatter with the pistachios and dill. Serve immediately (the butter will harden if left at room temperature for too long).