Place carrots, garlic and thyme sprigs (you don’t need to remove the leaves) in a medium bowl. Toss with 1 tablespoon of olive oil and sea salt and pepper.
Spread onto a baking sheet.
Roast for 40 to 45 minutes or until very tender. Let cool.
Place cooled carrot mixture (remove thyme leaves from stems) into the bowl of a food processor and add feta cheese and additional tablespoon of olive oil. Process until smooth. Add a bit more olive oil if needed. Season with sea salt and pepper.
Transfer to a bowl and refrigerate. Remove from the refrigerator about 30 minutes before serving.
(If you have time I recommend making it a day in advance so the flavors can meld.)
Serve with sliced bread or crackers.
Notes
* You can use goat cheese in place of feta cheese.