Beat together eggs, yolks, sugar, honey, and salt in a saucepan until evenly blended then whisk in milk. Cook over low, stirring frequently, until the mix is thick enough to coat the back of a spoon. Be careful to not allow it to boil.
Set aside to cool. The best way is by transferring the mix to a separate bowl, then by putting that bowl over a pan of ice water. Stir gently to help the heat dissipate and prevent a skin from forming.
Once it reaches room temperature, cover and refrigerate for 1 hour.
Pour the chilled custard, heavy cream, and vanilla into an ice cream maker, and process according to the manual. When done, either enjoy as soft serve right away, or freeze and enjoy later.
