Preheat a grill to high. In a bowl, combine 2 tablespoons room-temperature butter, 1 tablespoon each crumbled blue cheese and finely chopped shallot, and 2 teaspoons chopped fresh thyme. Slice a 1-pound log of prepared polenta into four 1 1/2-inch rounds and quarter each into wedges. Thread 4 polenta wedges and 3 stemmed shiitake mushroom caps alternately onto each of four 10-inch skewers. Brush with extra-virgin olive oil; season with salt. Grill on a well-oiled grate with the curved side of the polenta wedges down, basting with half of the butter mixture, until the polenta is crisp, about 7 minutes. Flip, baste with the remaining butter mixture and grill for 8 minutes.
