To build the sandwich from the bottom up, spread 1/2 tablespoon of butter on a slice of bread, spoon 1 tablespoon of cranberry chutney on top and smooth it out. Follow with a few slices of turkey and a couple slices of brie. Sprinkle with the walnuts and scatter some arugula leaves evenly over the top. Spread another 1/2 tablespoon of butter on a piece of bread and press it, buttered side down, into the sandwich. Repeat with remaining sandwich ingredients.

Heat a cast-iron or other heavy skillet over medium-low heat. Add 1 tablespoon of butter and let it melt, swirling the pan around to coat. Put the sandwich in the pan and weigh it down with a heavy pot or can (or wrap an ordinary brick in aluminum foil and set it on top to compress the sandwich). Toast for 1 minute, turn the sandwich over before the bread begins to burn and repeat. Cut the sandwiches in half before serving.