Boil potatoes until tender, mash finely, and set aside to cool.
Mix one beaten egg, butter, tarragon, lemon zest, salt, and pepper into the mash.
Combine the chicken with the potato mixture.
Prepare three bowls containing breadcrumbs, flour, and two beaten eggs.
Shape the mixture into 5cm logs, coat in flour, egg, and breadcrumbs, then chill for 30 minutes.
Heat 8cm of vegetable oil in a saucepan over medium heat.
Test the oil with breadcrumbs to ensure they sizzle and rise immediately.
Fry croquettes in batches for 2 to 3 minutes until golden-brown and drain on paper towels.
Sauté shallots and garlic in olive oil, add sugar, spices, vinegar, and tomatoes, then simmer for 15 minutes.
Serve the warm croquettes with the tomato chutney.