Heat the cream, milk, honey, salt, and vanilla paste in a medium-sized saucepan over medium-high heat for approximately 5 minutes, stirring frequently, until it just barely begins to simmer. Do not let it boil.
While the cream mixture is simmering, whisk the egg yolks in a bowl until smooth. Set them aside.
Pour 1 ½ cups of the warmed cream mixture into a measuring cup.
Gradually whisk the cream mixture into the eggs while constantly stirring as you pour it into the bowl. Continuous whisking is paramount to prevent the eggs from curdling.
Pour the egg and milk mixture back into the saucepan while stirring constantly with a wooden spoon. Cook over medium heat for approximately 10 minutes (stirring constantly) until it is slightly thickened or it registers 180 degrees F. As you are stirring, ensure that you are scraping the bottom edge of the pan as it thickens. The mixture should produce “milk bubbles” on the edge of the pan, which is a good indication of proper temperature. Do not let it boil, as this will scald the cream and milk.
Pour the cream mixture into a heat-proof cup and let it cool on the counter for 30 minutes. Cover it with a lid or stretch film and refrigerate for at least 3 hours or for up to 24 hours.
Churn the mixture after it has chilled according to the ice cream manufacturer’s instructions. Mine takes about 15-20 minutes, and in the end, the mixture resembles the texture of soft-serve ice cream.
Transfer it to an airtight container and cover it tightly. Freeze it until firm for at least 3 hours, preferably overnight. Serve when chilled.