Preheat the oven to 375 degrees farenheit.
In a measuring cup or small bowl, mix the spices with the minced garlic, water and oil; set aside.
Trim fat from the chicken pieces, and place them in a large bowl. Pour the spice blend over the chicken, and rub it into all of the pieces really well. Add the potatoes and carrots to the bowl and set the mixture aside for at least 30 minutes, while you start the creamy garlic sauce (directions below).
Put the sliced leeks into a small bowl with the lemon zest and a shake of salt and toss.
Line a baking sheet with parchment paper and spread the chicken, carrot and potato mixture evenly across the pan. Cook in the oven for 20 minutes. Leaving the oven on, pull out the rack with the sheetpan, flip the chicken pieces and top everything with the leek and lemon zest mixture. Roast for another 30 minutes.
Serve with the creamy garlic sauce.