Cut the pears lengthwise into quarters, scoop out the cores, and trim off the stems.
Melt 2 tablespoons of the butter in a wide pan over medium-high heat. Add 1 pear (4 quarters), cut-sides down, to the pan and cook until lightly caramelized, about 2 minutes. Rotate and caramelize the other cut sides for another 1 to 2 minutes, until tender but not mushy.
Transfer to the bowl of a food processor fitted with a metal blade. Add the champagne vinegar, honey, and ½ teaspoon salt. Blend until completely pureed. Then, with the motor running, slowly drizzle in the oil and continue blending until the dressing is emulsified.
Cut 1 pound (455 g) of the Brussels sprouts in half. Doing so will cause some of the outermost leaves to fall off. Keep the loose leaves in a little pile on your cutting board.