Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper.
Pour olive oil into a small saucepan over medium-high heat and cook until lightly simmering, about 1 minute. Add crushed red pepper and remove from heat; set aside. Let chile oil infuse while preparing the rest of the recipe.
Toss carrots, onion, whole garlic cloves, olive oil, salt, coriander, and turmeric together in a bowl. Transfer to the prepared baking sheet in an even layer.
Roast in the preheated oven until soft, tossing halfway through, about 30 minutes total. Remove from the oven and allow to cool.
Transfer cooked carrot mixture to a food processor and add tahini, honey, and additional salt, if needed. Blend carrot dip until smooth.
Spoon dip into a small serving bowl. Strain chile oil into a small dish and discard crushed red pepper. Drizzle oil to your preference on top of the dip and garnish with parsley.