Preheat oven to 400 degrees F. Line a 15x10-inch baking pan with foil; coat foil with cooking spray.
Place squash halves, flat sides down, in prepared pan. Brush with the melted butter and sprinkle with 1/2 tsp. salt and the pepper. Roast 10 minutes; cool. Cut squash crosswise at base of neck pieces, about 1/2 inch from edges of cavities.
Place squash neck pieces, flat sides down, on a work surface. Arrange chopsticks or wooden spoons lengthwise on opposite sides of each neck piece. Cut squash crosswise into 1/4-inch slices, stopping when knife reaches chopsticks or spoon handles to prevent slicing all the way through.
Stuff 1/4 cup of the onion mixture between squash slices.
Stir crushed croutons and chicken broth into remaining onion mixture; divide between squash cavities.
Return squash to pan and roast 20 to 30 minutes more or until tender. Top with additional thyme, if desired.
In a small saucepan heat butter over low heat until melted. Continue heating until butter turns a light golden brown.
In a large skillet, heat oil over medium-low heat. Add onion, salt and pepper. Cook, covered, for 13 to 15 minutes or until onions are tender, stirring occasionally. Uncover; cook and stir over medium-high heat for 3 to 5 minutes more or until golden.