Place the wheat berries and chicken broth in a medium saucepan with a good pinch of kosher salt. Bring to a boil, then lower to a simmer. Simmer for 35-45 minutes until tender. (Wheat berries can vary slightly in cooking time, so I recommend tasting a few at the 35 minute mark and going from there.) Strain the wheat berries (they’ll absorb a lot of the broth as they cook, but not all of it), and let them cool to room temperature.
Meanwhile, heat the olive oil in a medium skillet over medium heat. When hot, add the onions and a pinch of salt, and cook for about 5 minutes until softened and lightly browned. Set aside and let cool to room temperature.
In a large mixing bowl, whisk all the ingredients for the dressing.
Add the shredded chicken and toss to coat. Add the cooled wheat berries and onions and toss again. Add the arugula, Brussels sprouts, cilantro, mint, green onions, and jalapeños, and toss one more time. Taste and season with a little extra salt (if necessary) and plenty of fresh ground pepper. (If you like things extra lemon-y like I do, feel free to add an extra squeeze of fresh lemon juice.)
Serve salad at room temperature or chilled.