Step 1

Preheat oven to 350°. Place parsnips in an 8x8" baking dish or medium ovenproof skillet. Cover tightly with foil or a lid and bake until very soft and mashable (like a baked potato), 45–60 minutes. Let cool, then coarsely chop.

Step 2

Meanwhile, toast hazelnuts on a rimmed baking sheet, tossing once, until golden brown, 7–10 minutes. Let cool, then coarsely chop.

Step 3

Blend dill and grapeseed oil in a blender until smooth. Transfer to a small bowl.

Step 4

Purée chiles, garlic, feta, and lemon juice in a food processor until smooth. Add parsnips and pulse until mixture looks mostly smooth. With motor running, stream in olive oil and process until mixture is extremely smooth and aerated. Transfer dip to a serving bowl; top with hazelnuts and drizzle with dill oil.

Step 5

Do Ahead: Dip (without hazelnuts and dill oil) can be made 3 days ahead. Cover and chill.