Instructions: Combine kosher salt and sugar in large container with 4 cups cold water and stir to dissolve. Add chicken and soak for 1 to 2 hours at room temperature (if weather is hot, refrigerate).

Preheat oven to 450 degrees. Drain chicken and pat dry. Put garlic, thyme and 2 tablespoons butter in chickens cavity, season bird with salt and pepper, and truss it.

Combine remaining 2 tablespoons butter with oil in large ovenproof skillet or roasting pan and turn heat to medium-high. When butter melts, brown chicken on both sides, coloring one leg and half the breast at a time; move chicken occasionally to prevent sticking, and regulate heat so skin browns but does not burn - it will take about 5 minutes per side. Split 1 vanilla bean; scrape out seeds and spread them on chickens breast, and insert pod into cavity. Put chicken on its back and put pan in oven.

Roast 35-45 minutes, basting occasionally with pan juices, until bird is nicely browned and instant-read thermometer inserted into its thigh reads 155 degrees.

Meanwhile, to make olive sauce, combine olives, cumin, cardamom, coriander and stock in small saucepan. Split remaining 2 vanilla beans and add them; bring to boil, turn off heat and keep warm; if sauce becomes too thick, thin with a little more stock. Just before serving, season to taste.

To make yogurt sauce, combine yogurt and mint in blender; puree. Season with salt and pepper.

When chicken is done, remove from oven, let rest for a couple of minutes, and carve; serve with the two sauces.

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