1. Preheat oven to 350°. Toast almonds on a rimmed baking sheet, tossing halfway through, until slightly darkened and fragrant, 8–10 minutes. Let cool; set aside.
2. Cut any thick carrots in half lengthwise, then slice all carrots crosswise into 4 pieces. Toss on a parchment-lined baking sheet with 2 Tbsp. oil and 1 tsp. salt. Spread carrots out evenly on baking sheet and roast, stirring once or twice, until very tender and starting to shrivel and brown (but not char), about 1 hour.
3. Transfer carrots to a food processor; add garlic, chickpeas, lemon juice, pepper, paprika, chopped parsley, ½ cup oil, 1½ tsp. salt, and reserved almonds. Process, adding more oil as needed, until mixture is almost completely smooth. Taste dip and add more lemon juice and/or salt if needed.
4. Transfer dip to a small bowl, drizzle with more oil, and top with parsley leaves.

Do Ahead: Dip can be made 1 week ahead. Cover and chill.