Toast pistachios on a small rimmed baking sheet until golden, about 5-7 minutes. Halve squash halves again, this time horizontally. Toss the squash and shallots with a tablespoon oil, maple syrup, and the pepper. Scatter onto a baking sheet (making sure the squash is sitting cut-side down), and roast until caramelized, about 20-25 minutes. Remove any shallots that are browning too quickly.
Meanwhile, combine the herbs, lemon juice, and ⅓ cup olive oil in a blender. Blend until smooth, then season to taste with salt.
Blanch the turnip greens in a large pot of salted boiling water until just wilted, about a minute. Spread out on a baking sheet, and when cool enough to handle, wring greens out of any excess water. Chop into 1” pieces.
Warm remaining 3 tablespoons in your largest cast-iron or nonstick skillet set over high heat. Add the wheat berries in an even layer, and, press down with a spatula. Allow to cook undisturbed until crispy, about 7-10 minutes. (Fight the urge to check too early!, but if the wheat berries start to get too dark, reduce the heat to medium.) Flip the wheat berries over in large crusty pieces, and continue to crisp, another 2-3 minutes longer.
Transfer crisped wheat berries to a large serving bowl. Fold in pistachios, caramelized shallots, turnip greens, and herb dressing. Top with squash, and serve.