The key to brown butter is a watchful eye. Use a light-color saucepan so you can see the butter go from creamy pale yellow to golden brown.
Preheat oven to 450°F. In a shallow baking pan toss bread cubes with 1 tablespoon oil. Spread in an even layer. Bake for 8 minutes or until toasted, stirring once. Sprinkle with Parmesan and finely chopped parsley; toss to coat. Transfer to a piece of foil to cool.
In the shallow baking pan arrange squash in an even layer; drizzle with 2 tablespoons of the oil. Season with salt and pepper. Bake for 20 minutes. Add endive, radicchio, and 1 tablespoon oil and toss to coat. Season with additional salt and pepper. Bake for 10 minutes more or until vegetables are tender and browned.
Meanwhile, in a small saucepan heat the butter over medium-low heat until browned. Remove from heat. Stir in lemon juice and capers.
Arrange vegetable mixture on a platter. Drizzle with browned butter mixture and sprinkle with croutons and 2 tablespoons parsley.