How to Make It
In a medium saucepan, combine 1/4 cup of salt with the smashed garlic, the sugar, rosemary, bay leaf and 2 cups of water. Bring to a simmer, stirring to dissolve the salt and sugar. Transfer the mixture to a very large bowl and stir in 2 cups of cold water.
In a spice grinder, grind the mushrooms to a powder. (You should have about 3 tablespoons.) Whisk the porcini powder and buttermilk into the salt mixture. Place the chicken in the buttermilk brine, cover with plastic wrap and refrigerate for at least 6 hours or up to 12 hours.
Preheat the oven to 425°. Remove the chicken from the brine and pat dry; discard the brine. Tuck the wing tips behind the breasts, tie the legs with kitchen twine and set the chicken, breast side up, in a rack over a roasting pan. Season all over with salt.
Roast the chicken for 15 minutes. Brush the butter all over the chicken, then return it to the oven and roast for about 45 minutes longer, until an instant-read thermometer inserted in the thickest part of the thigh registers 165°. Transfer to a cutting board and let rest for 15 minutes.
Meanwhile, in a small skillet, simmer the olive oil with the sliced garlic over moderately high heat, stirring occasionally, until the garlic just starts to brown and the oil is hot and fragrant, about 3 minutes. Remove the skillet from the heat and let cool.
Carve the chicken and arrange the pieces on a platter. Brush with some of the garlic oil and serve right away, passing the remaining oil at the table.