Preheat oven to 375°. In an 8- or 9-in. square pan, toss bread with 1 tbsp. oil to coat. Bake, stirring once, until golden and crisp, 15 to 20 minutes.
Meanwhile, toast caraway seeds in a large frying pan over medium heat until fragrant, 3 to 4 minutes. Pour into a food processor and set aside.
Cook pancetta in frying pan over medium heat, stirring occasionally, until browned, 5 to 10 minutes. Let cool in pan to room temperature.
In food processor, whirl caraway seeds 1 minute to break up a bit. Add remaining 3 tbsp. oil with 1/4 cup pickles, the vinegar, and pepper and whirl until blended. Add egg yolk; whirl until creamy and a little frothy, 30 to 60 seconds. Scrape dressing into pan of pancetta and stir to loosen browned bits.
In a salad bowl, toss mustard greens with remaining pickles and half the dressing. Add croutons and cheese and toss again. Serve with more dressing on the side.
*Dense, artisan-style bread is especially good here. If you're worried about the risk of salmonella from consuming raw eggs, use pasteurized egg whites, available at well-stocked grocery stores.