Add the olive oil to a small saucepan and heat over medium-high heat until hot, about 2 minutes. A couple wisps of smoke are okay but it shouldn't be smoking. You can also test with a wooden chopstick (or any wooden utensil) by dipping it in the oil to see if it simmers.
To a small bowl, add the dill and red pepper flakes. Carefully add the oil over. Set aside.
For the Carrot Dip
Preheat the oven to 400 F (205 C) and line a sheet pan with parchment paper.
Add the carrots to the prepared pan and toss with 1 tablespoon of the dill oil, 1/8 teaspoon salt, and 1/8 teaspoon black pepper.
Cover with foil and bake until the carrots are beginning to tender, 25 to 30 minutes. Uncover and bake until the carrots have developed some wrinkled and light golden spots, about 10 minutes.
Transfer the carrots to a food processor. Add the chickpeas, lemon juice, reserved chickpea liquid, paprika, garlic powder, 3/4 teaspoon salt, 1/4 teaspoon pepper.
Swirl the dip into a shallow bowl and top with the dill oil and more fresh dill .
Notes
Note 1: You can substitute the reserved chickpea liquid (aquafaba) with broth or water.