Put lemons cut-side down with tongs on a hot grill or cast-iron pan. Let them cook until the cut side is charred and they are warmed through.
In a small bowl, whisk the juice of the lemon, an equal amount of olive oil, about a ½ teaspoon of mustard, and your shallot. Season to taste with salt and fresh ground pepper. For an extra kick, add some zest of the lemon.