Pour 1 cup of the heavy cream in a medium bowl. Add the matcha and whisk until smooth. Set a fine mesh sieve over the bowl.
In a medium bowl, whisk the egg yolks until smooth.
Add the remaining heavy cream, milk, sugar, and salt in a saucepan and heat on medium, stirring to combine and dissolve the sugar. Continue cooking and stirring often until the mixture begins to thicken and bubble around the edges (about 3 minutes). Make sure it doesn't start to boil though.
Turn the heat to low and measure out one cup of the hot milk mixture and slowly pour it into the bowl with the egg yolks, whisking constantly. This is to prevent the eggs from cooking (nobody wants scrambled eggs in their ice cream). Slowly pour the combined egg yolks and milk back to the saucepan, stirring constantly as you do so. Turn heat to medium-low.
Continue cooking until the mixture thickens (about 4 to 5 minutes). To test, dip a wooden spoon in and check to see if you can draw a clear line with your finger. The line should stay as it is and not loose its shape.
Pour into the fine mesh sieve over the reserved heavy cream and matcha and stir together.
Fill a sink with ice and cold water and put the bowl in it, bringing it to room temperature (about 15 to 20 minutes).
Cover and chill for at least 4 hours in the refrigerator.
Place a loaf pan in the freezer. Transfer chilled ice cream to an ice cream maker and follow the directions of the manufacturer (20 minutes for mine).
Once done, quickly transfer 1/3 of the ice cream into the frozen loaf pan. Drizzle with sweet red bean paste. Repeat until you've used up all the ice cream. Use a skewer or spoon handle and drag it back and forth along the top layer, making swirls.
Cover with plastic wrap and freeze for at least 4 hours before serving. Let the ice cream sit out for 10 minutes before scooping it up.