For the croutons: Preheat the oven to 350 degrees F; position an oven rack in the middle of the oven.
In a large bowl, toss the bread cubes with the olive oil, salt and pepper. Spread the bread cubes on a rimmed baking sheet and bake until golden brown, 8 to 10 minutes. Let cool. (The croutons will keep in an airtight container for up to 3 days.)
For the escarole: Preheat a grill on medium heat.
Cut the escarole head in half, then wash and dry. Grill the escarole cut-side down to give it a little char, about 3 minutes. (Do not flip and cook the other side. We are looking for just some of the escarole to be charred.) Set aside and let cool.
For the warm anchovy vinaigrette: In a small saucepot, heat 1 tablespoon olive oil over low heat until shimmering. Add the shallots and anchovies and cook, stirring, until the shallots have softened and the anchovies fall apart and dissolve in the oil, 2 to 3 minutes. Stir in the red pepper flakes. Add the vinegar and cook, stirring, until it has reduced slightly, about 1 minute. Whisk in the remaining 4 tablespoons oil.
Cut the escarole into 1-inch pieces and put in a large bowl. Add the vinaigrette and croutons and toss to combine. Season with salt and pepper.