Heat the oven to 400 degrees. Place either parchment paper or tin foil on a baking sheet.
Melt butter and set aside. Cut carrots in half lengthwise and place on the baking sheet. Drizzle carrots with melted butter and season carrots with salt and pepper.
Once oven is heated, place carrots in the oven for 35-40 minutes.
As the carrots roast, mince the shallot and garlic. In a bowl, mix shallot and garlic along with goat yogurt, spices, and lemon juice. Season with salt & pepper. Set aside.
Chop pistachios into small pieces and remove leaves from mint sprigs. Discard the stems.
Once carrots have roasted for 20 minutes, remove them from the oven. Arrange carrots on a plate with a set of tongs.
Drizzle carrots with the yogurt sauce. If you want to thin the sauce further, you can always add more lemon juice.
Garnish carrots with mint leaves and pistachios. Enjoy warm from the oven or room temperature.