Preheat oven to 400ºF. Cut carrots on a diagonal into 2" pieces.In a large mixing bowl, combine 2 Tbsp. olive oil, coriander, cumin, salt, and black pepper; mix to combine. Add carrots and toss until fully-coated. Spread carrots on a large rimmed baking sheet, avoiding any overlap. Roast carrots for 33 to 38 minutes, tossing once halfway through, until lightly charred and deeply caramelized.
To the same mixing bowl (no need to wipe it clean), add remaining 3 Tbsp. olive oil, parsley, capers, and garlic; mix well.
Add pistachios and sesame seeds to a dry skillet over medium heat. Lightly toast nuts and seeds, tossing often, until aromatic, about 3 to 5 minutes. Transfer to a bowl and season with a pinch of salt.
Use a spatula to transfer roasted carrots from the baking sheet to the bowl with parsley mixture; toss to combine.
Spread roasted carrots on a serving platter, and scatter pistachio-sesame mixture overtop.
