Heat oven to 425°F. Toss cauliflower with oil, 1/2 teaspoon salt, paprika and pepper, spread on a rimmed sheet pan and roast for 30 to 35 minutes, turning once, until tender with deeply browned edges.
Meanwhile, toss carrot ribbons with vinegar, water, sugar and remaining salt in a bowl. Stand for 20 minutes, turning once, then drain thoroughly and blot lightly.
Blend feta, yogurt and lemon zest in a small processor until thick and fairly smooth. Refrigerate while the cauliflower finishes roasting.
Let roasted cauliflower cool for 5 minutes so visible steam subsides. Split the rolls and toast only their cut faces under the broiler for 1 to 2 minutes.
Spread whipped feta along both cut faces. Divide cauliflower over the bottoms, pressing the florets gently into the spread, then add drained carrot ribbons.
Close the rolls around the filling and cut across the middle. Serve one sub per person while the cauliflower is still warm and the pickled carrots are crisp.