Mix the goat cheese, potato, cream, herbs, yolk, paprika and a grind of pepper in a bowl. Mix well till incorporated.
Prepare a tray with baking paper ready to lay the goat croquettes on once rolled. Take a scoop of the potato mixture, approximately the size of a golf ball from the bowl and roll firmly with your hands. (I made a longish almost flat shape so the croquettes cook in a small amount of oil and turn easily.) The mixture should not be wet, it will stick together easily. If you find that your mixture is wet due to the potatoes holding water you may need to add the 1 Tablespoon extra flour.
Keep rolling the mixture till you have evenly sized ovals on the tray. Check to make sure they are all the same size by pinching off a bit here and there to even them out, reshaping as you go.
Refrigerate till firm and well chilled ( 1 hour or more).
Whisk the egg with the milk . Put the flour onto a flat plate and season with a little salt. Put the crumbs onto a flat plate and prepare to crumb the croquettes. Arrange the croquettes first followed by the flour, egg wash and crumbs and position another tray at the other end. Crumb the oval croquettes and then chill again until needed. ( Up to 4 days ahead)
Heat a skillet or fry pan then add half the oil. Shallow fry in batches turning once golden on each side . Drain on paper towel and serve immediately.