Carrots add a pretty orange hue and subtle sweetness to this smooth and creamy hummus. Choose milder red chiles, such as New Mexico-style or guajillo dried chiles, for heat that's not overpowering.
Bring carrots, stock, chiles, and garlic to a boil in a small saucepan over medium-high. Cover and reduce heat to medium-low; simmer until carrots are very tender, 15 to 20 minutes. Drain.
Process carrot mixture, tahini, mint, lemon juice, coriander, and cumin in a food processor, stopping to scrape sides as necessary, until very smooth, about 2 minutes. Transfer to a bowl, and stir in salt and pepper. Cover and chill 4 hours or up to 2 days. Before serving, drizzle with olive oil and sprinkle with sesame seeds, if desired. Serve with flatbreads and crudités.