Cut the carrots in chunks and put them in a sautee pan with the garlic and 1 tbsp of oil. Saute 3-5 minutes at medium heat.
Add the chicken stock and let simmer until the carrots are very tender, around 8-10 minutes.
Add the spices, except for salt, and let cook for another 1-2 minutes or until most or all of the stock has disappeared.
Transfer the contents of the pan to a food processor and blend while you drizzle in the last 2 teaspoons of olive oil. Only blend until the ingredients start to come together - you don't want the mixture to be totally smooth.
Add the olives and pulse a few times. Taste to see if the flavor and texture is right.
Adjust seasoning if necessary. If your paste is too thick, add a bit of water. If desired, add a bit of salt and then pulse a few more times.
Serve warm, or transfer to an airtight container for storage in the fridge for up to a few days.
I add the olives after the first round of blending, because I like to have little chunks of olive in the mix. If you prefer a smooth paste, just add the olives right when you transfer the carrots to the food processor.