Combine first 4 ingredients in a small saucepan over high heat; bring to a boil. Reduce heat; cook until reduced to 1/2 cup (about 8 minutes), stirring occasionally until sugar dissolves. Drain mixture through a fine sieve into a bowl, reserving cooking liquid; discard solids. Cool.
Melt brown sugar and butter in a large nonstick skillet over medium-high heat. Cook 2 minutes. Stir in chopped thyme, juice, and salt. Add pears, cut-side down, to pan. Reduce heat to low; cook 2 minutes or until tender, turning once.
Arrange 2 pear wedges on each of 4 plates; drizzle pears evenly with pan juices. Sprinkle 2 tablespoons cheese over each serving; top each serving with 2 tablespoons reserved cooking liquid. Sprinkle with black pepper. Garnish with thyme sprigs, if desired.