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1. Combine heavy cream and buttermilk in a medium saucepan. Place over medium-low heat and allow to warm to barely a boil (try not to allow milk to boil).
2. Meanwhile, combine eggs, egg yolks, sugar and honey in a medium mixing bowl (something with some weight), and whisk thoroughly.
3. You want the milk mixture to be at about 150 degrees F in order to combine it with the egg mixture, so you may want to turn off the burner, mixing constantly to allow mixture to cool slightly.
4. Once milk is at desired temperature, use heatproof measuring cup with a spout to take about a cup out of the pot.
5. While whisking sugar/egg mixture, SLOWLY and simultaneously pour in warm milk. (Try putting the bowl on a rubber hot plate so it doesn't spin and splatter everywhere while doing this.) This allows the eggs to combine with the heated milk and cook ever so slightly. Be sure not to dump milk into eggs for fear of flash cooking them, which will result in an ice cream that tastes like an omelet.
6. Pour combined egg/milk mixture back into pot, turn burner on low and, while whisking constantly, allow mix to heat up a bit; it only needs another 2 minutes, tops. You want it to thicken slightly, until it coats the back of a spoon.
7. Pour in a heat-resistant bowl and cover with plastic wrap, then allow to chill overnight or for 4-5 hours before you run it in your mixer.
8. Remove cherries from their syrup, but reserve liquid for later.
9. Puree cherries in a food processor until smooth.
10. Push pureed cherries through a food mill or strainer in order to make cherry mix as smooth as possible. (You will end up losing about 1/3 of the cherries this way, which is fine.)
11. When you finally run your custard through your mixer, allow it to run for about 25 minutes, or just until fully churned. Pour 1/2 of the reserved cherry syrup and pureed and strained cherries into ice cream maker for the last 5 minutes, adding more syrup if desired.
1. Place cherries into a wide-mouthed bowl.
2. Bring water and salt to a boil, stirring until salt is dissolved. Let cool for 10 minutes, then pour over cherries. Cover and let sit 12 hours or overnight.
3. Drain cherries, discarding brine, and rinse in cold water. Set aside.
4. In a medium saucepan, combine sugars and lemon juice. Bring just to a boil, stirring to dissolve sugar, and remove from heat.
5. Pour over cherries, cover and let stand for 24 hours.
6. Drain cherries, reserving juice. Set cherries aside.
7. Bring reserved juice to a boil again. Allow to simmer for a short time in order to thicken.
8. Remove from heat and stir in almond extract. Pour juice over cherries.