Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper and spread chopped carrots in a single layer. Drizzle with 1 tablespoon olive oil and season with a pinch of salt. Toss to coat evenly.

Roast carrots for 25-30 minutes, stirring halfway through, until tender and lightly caramelized. Remove from oven and let cool for 5 minutes.

Add roasted carrots to a food processor along with chickpeas, tahini, lemon juice, garlic, cumin, remaining olive oil, and salt. Blend on high for 1-2 minutes until smooth.

While processor is running, slowly add cold water one tablespoon at a time through the feed tube. Continue blending until hummus reaches desired creamy consistency, about 2-3 minutes total.

Taste and adjust seasonings as needed. Add more lemon juice, salt, or cumin to preference. Blend again briefly to incorporate.

Transfer to a serving bowl, create a shallow well in the center, drizzle with olive oil, and sprinkle with paprika if desired. Serve immediately or refrigerate until ready to use.