Combine porcini mushrooms with 1 cup boiling water and let stand for 20 minutes. Drain and rinse; chop finely and set aside.
Heat oil in a small skillet over very low heat. Add unpeeled garlic; cook stirring often, for about 10 minutes or until softened and skins are golden.
Remove from skillet; let cool slightly. Squeeze garlic out of skins into large bowl, mashing with the back of the spoon.
Add porcini mushrooms, ground beef, tarragon, salt and pepper to garlic; lightly combine. Form into 6 thick patties. Grill patties over medium-high heat for 5-7 minutes per side, or until rapid -read thermometer inserted sideways into center of each reads 160°F.
Meanwhile, grill sides of buns until lightly golden. Place arugula on bottom halves; top each with cooked patty. Top each patty with goat cheese, tomato slice, and bun on top.