Heat a skillet over medium heat. Add 1-2 teaspoons olive oil. Add the onions, season with salt and pepper, toss to coat. Reduce heat to medium low and cook, stirring often, until brown and caramelized, about 45 minutes.
While onions are cooking, place pear slices in a single layer on a lined baking sheet. brush with a little olive oil and lightly season with salt and pepper. Drizzle with honey. Bake until tender, 20-25 minutes, rotating pan halfway through.
To assemble sandwiches, spread softened butter on one side of a slice of bread, and be sure to cover all the way to the edges. Place butter side down. Top with shredded cheese, then onions, then layer with pear slices. On a second piece of bread, spread butter on one side and chevre on the other side. Place chevre side on top of the pears, butter side up.
Heat a skillet over medium low heat. When hot, place sandwich in pan and cook until cheese starts to melt and outside of bread is golden. Flip and repeat.
The exact amounts of cheese, onions, and pears that you put on each slice of bread is up to you, and also will depend on the size of your bread. I ended up using about 1/3 cup shredded cheese, slightly less than an ounce of chevre, three slices of pears and about a tablespoon (maybe slightly more) of caramelized onions per sandwich.