1Preheat oven to 450 degrees. Place 1/2 cup walnuts in a small saucepan and add water to cover by 1 inch. Bring to a simmer. Reduce heat and simmer until slightly softened, about 20 minutes. Drain and let cool to room temperature.
2Meanwhile, toss the cauliflower in a bowl with oil and 1/4 tsp. salt. Spread in a single layer on a baking sheet. Roast until browned on the bottom, about 20 minutes. Transfer to a large bowl and let cool to room temperature.
3Blend the cooled walnuts, tahini, 1/4 cup lemon juice and water in a food processor until very smooth, scraping down the sides a few times. If it's too thick to blend, add additional room temperature water by the tablespoon until you get a thick sauce.
4Toast the remaining 1/2 cup walnuts in a small dry skillet over medium heat for about 5 minutes. Chop and add to the cauliflower along with dill, shallot and the remaining 1/2 tsp. salt. Add the dressing; gently toss to coat. Season to taste with more lemon juice, if desired. Serve at room temperature.