Bring a large pot of water to a rapid boil, then season with kosher salt. Add the trimmed broccoli rabe, then cook. While it’s cooking, prepare an ice bath. Place cold water and ice in a large bowl. Cool.
In a small bowl, combine extra virgin olive oil, aged balsamic vinegar, Dijon, kosher salt, and black pepper. Whisk well. Stir in chopped shallot.
Drain the broccoli rabe, squeezing out as much water as possible, then transfer it to a cutting board. Chop into 1-2-inch pieces. Using your hands, tear the mozzarella into small bite-size pieces, then add directly to the bowl. Add chopped roasted red peppers.
Squeeze half of a lemon on top, then pour on the dressing. Give the salad a good toss, then taste and adjust seasoning as needed. I like to transfer to a large serving bowl before sprinkling with flaky sea salt. Enjoy hot or room temperature!