Navy makes this dish with fresh flageolet beans, but we substituted easier-to-find dried beans here.
Preheat oven to 375 degrees. Combine cauliflower, 1 tablespoon oil, chili powder, and agave on a rimmed baking sheet. Season with coarse salt; toss to combine. Spread in a single layer and roast until cauliflower is tender and golden brown in spots, about 25 minutes. Transfer to a bowl; let cool slightly.
Add beans, lemon juice, and remaining 2 tablespoons oil to bowl. Toss to combine. Divide mixture evenly among 4 plates. Top with turnips and pistachios. Drizzle with oil, sprinkle with flaky salt, and serve.