Toss beets, both cucumbers, scallions, both chiles, lemon zest, ricotta salata, and herbs in a large bowl to combine.
Add vinegar, sugar, and 2 tsp. poppy seeds, season with salt and pepper, and drizzle with oil. Toss salad gently to coat. Taste and drizzle with more vinegar if needed.
Transfer salad to a platter, lightly drizzle with more oil, and sprinkle with more poppy seeds.