Preheat oven to 425°F. Coat two baking sheets with cooking spray.
Place cauliflower, potatoes, oil, 3/4 tsp. of the salt, 1/2 tsp. of the black pepper, coriander, and cumin in a large bowl; toss to combine. Spread mixture evenly on baking sheets, avoiding any overlap. Bake for 30 to 40 minutes, tossing once halfway through, until tender. Let cool for 10 minutes. Transfer to a bowl.
Combine tahini, lemon juice, and water in a small bowl; whisk to combine. Add tarragon, sugar, vinegar, garlic, remaining 1/4 tsp. salt and black pepper; stir to combine. Pour tahini sauce over potato mixture; toss to combine. Add arugula; gently toss to combine.