Create an ice bath: Fill a large mixing bowl with 15 pieces of ice and a splash of water. Set a slightly smaller bowl inside the large bowl, then fit a sieve or strainer inside the smaller bowl. Set the ice bath aside.
In a small saucepan, heat the honey on medium heat. Stir in salt and cinnamon until fragrant and combined. Remove the pan from heat and set aside.
In a medium mixing bowl, whisk together the 4 egg yolks. Set aside.
In a medium saucepan, combine the milk and sugar. Heat over medium heat until the sugar has dissolved and the milk simmers gently. Remove the pan from the heat.
Temper the milk mixture: Whisking continuously, pour 1/4 of the milk mixture into the whisked egg yolks. Pour slowly and in small batches so as not to cook the eggs with the hot milk. This helps to raise the eggs’ temperature slowly.
Return the egg and milk mixture to the medium saucepan and place over low heat. Stirring continuously, heat the mixture until the thermometer reads 170 to 175 degrees. Turn off the heat when the mixture appears thick and coats the back of the spoon.
Into the ice bath, pour the mixture through the sieve into the small bowl. If the honey has cooled and thickened, rewarm it and stir it into the egg yolk mixture, mixing thoroughly. Stir in the heavy cream.
Chill for 4 hours, or overnight.
Pour the mixture into the bowl of your ice cream maker. Churn it according to your ice cream maker’s instructions. Serve immediately for soft serve, or alternatively transfer the ice cream to a freezer-safe container and freeze overnight. Serve with honey drizzled on top.