Mix together carrot, onion, salt, pepper, flour, and egg. If necessary, add more flour a little at a time, until a cohesive, but not overly wet batter is formed.
Heat oil in a frying pan with deep sides over medium-high heat. Once oil is heated through, carefully drop fritter batter by the 1/4-cup full into the pan, and fry on each side for approximately 4 minutes per side, turning down the heat as necessary to maintain oil temperature. Remove cooked fritters to a rack or paper-towel lined tray to drain and repeat until all batter is used.
To make the sauce, whisk together remaining ingredients. Serve with fritters.
Notes
If deep frying, fill a fryer to marked level, or add 2 inches of cooking oil to a deep nonreactive pan such as enameled cast iron.