Set up your grill for even medium-high heat. If using a charcoal grill, distribute the coals evenly. If using a gas grill, heat both sides evenly.
In a small saucepan set on the grill, melt the butter with the clove of smashed garlic. Remove the garlic.
Place the torn baguette in a mixing bowl and pour the melted garlic butter over the top. Toss to coat the bread and season with salt and pepper. Put the croutons in a cast-iron pan and place on the grill. Cover the grill and bake until golden brown and crisp, 5 to 7 minutes.
In the meantime, in a mason jar, add the lemon juice, olive oil, grated garlic, anchovies, Dijon and red pepper flakes. Season with salt and pepper and vigorously shake to combine.
Remove the croutons from the grill and set aside. Brush the kale leaves and the cut side of the endive and escarole with some of the lemon vinaigrette. Place on the grill, cut-side down, and char for about 2 minutes.
Remove from the grill, slice into bite-sized pieces and put in a large serving bowl. Add the croutons and chives and dress with the remainder of the vinaigrette. Add Parmesan and toss to combine. Serve.