Add the bacon to the skillet and cook, stirring occasionally until crisp, 5 to 10 minutes.
Trim and chop the endive and radicchio and put them in a large bowl. Then trim, peel, and mince the shallots.
When the bacon is crisp, transfer it to the towels with a slotted spoon. Add the shallot to the skillet and stir until it sizzles. Turn off the heat and pour off all but 2 tablespoons of the fat, leaving the shallot in the pan.
To make the dressing in the skillet, whisk in 1 teaspoon Dijon mustard, 1/4 cup olive oil, 3 tablespoons balsamic vinegar, and a sprinkle of salt and pepper.
Pour the dressing over the endive and radicchio, add the cooked bacon, and toss. Taste and adjust the seasoning, and serve.