1. Preheat your oven to 400 degrees F. In a medium bowl, toss bread pieces with 2 tablespoons of the olive oil. Spread out onto a baking sheet and bake for about 7 minutes, or until "semi-crisp". Remove from the oven and set aside, but leave the oven on.
2. Heat a large cast-iron skillet over medium heat and add the remaining 2 tablespoons of the olive oil. Add the endive halves, turn the heat to high, and cook, turning occasionally, until the endives are slightly browned on all sides. Add 1/3 cup water to the pan along with the butter, and cook for a few minutes until the liquid has reduced by half.
3. Tuck the anchovies around the endive halves and scatter the thyme leaves and the parsley over the top, along with the breadcrumbs. Drizzle the remaining 1 tablespoon of the olive oil over the top, season with salt (if using the anchovies, I wouldn't add much, if any) and pepper, and transfer the skillet to the hot oven. Bake for about 25 minutes, or until the endive is very tender when pierced with a fork. Add more fresh pepper and a squeeze of fresh lemon juice, and garnish with additional thyme and fresh parsley before serving, if desired.