In a saucepan, heat olive oil over medium-low heat. Add the onion, and sauté for 5 minutes. Add garlic, coriander seeds and half of one Serrano chili. Sauté until all ingredients are soft but not browned, another 3 minutes. Add a pinch of salt.
Add carrots and potatoes, and stir. Add chicken stock, and bring to a simmer until the carrots and potatoes are soft, about 15 minutes.
Purée in a food processor in 2 or 3 batches, and pour into a large bowl. Strain the soup through a mesh strainer, pressing on the solids, back into the clean saucepan. (You can put through the strainer a second time if your soup has too much texture.) Warm the puréed soup.
Add a squeeze of fresh lime juice and season to taste with salt and pepper. Finish soup with a drizzle of lime oil, a sprinkle of fresh cilantro and couple slices of Serrano chili.