In a small pot, simmer the cream, milk, sugar and salt until sugar completely dissolves, about 5 minutes. Remove pot from heat. In a separate bowl, whisk the yolks and matcha until they're broken up.
Whisking constantly, slowly whisk about a third of the hot cream into the yolks, then whisk the yolk mixture back into the pot with the cream. Return pot to medium-low heat and gently cook until mixture is thick enough to coat the back of a spoon (about 170F on an instant-read thermometer).
Strain through a fine-mesh sieve into a bowl and toss any matcha or scrambled egg bits that get caught in the sieve. Cool to room temperature. Cover and chill at least 4 hours or overnight. Churn in an ice cream machine according to manufacturers’ instructions. Serve directly from the machine for soft serve, or store in freezer until needed.
If you want these popsicles to be super clean, transfer the ice cream into a piping bag. Otherwise, use a spoon. Pipe or spoon the matcha ice cream into the molds until they’re half full.
Cherry Rosewater Compote
Blend everything with 2 T water until the cherries are broken down. You may need to add more water depending on how powerful your blender is. Pour on top of the matcha ice cream, stick popsicle sticks in the center, and freeze until solid, preferably overnight.
To unmold, run the bottom part of the mold under warm water (if you dip the bottom of the popsicles in warm water, this also works), and wiggle the popsicle out of the mold once the mold warms up a bit.