Whisk the eggs in a bowl and set aside.
In another bowl, mix together the flour, sugar and salt.
In a heavy 3 quart saucepan, heat the milk over medium low and gradually add sugar mixture, stirring constantly for about 8 minutes or until it thickens to the consistency of thin gravy. It will not be as thick as pudding or cream gravy at this point, but it will be slightly thicker and smoother than when you began.
Whisk about a fourth of the milk mixture into the eggs, then pour the egg/milk mixture back into the saucepan and continue stirring for about 2 minutes or until eggs are fully incorporated and mixture is slightly thicker. If you have any lumps (such as bits of eggs), pour through a sieve. If no lumps, pour directly into a bowl. Let cool slightly at room temperature than chill for several hours.
Add the half & half and the vanilla to the custard mixture and freeze in batches per your ice cream machine’s directions. Towards the end of the cycle, pour in the honey (if making in batches, use a fraction of the honey for each batch) and let the machine mix it a bit, then remove the dasher and stir mixture until honey is fully blended.
Pour the ice cream into containers and freeze until firm enough to scoop.