Freeze the ice cream maker bowl at least 24 hours in advance. Shake before using—if you hear liquid inside, freeze longer.
In a medium bowl, sift the matcha powder. Add 3–4 tablespoons of the soy or oat milk and stir into a smooth paste. Continue adding the milk in small splashes (about 3–4 tablespoons at a time), stirring until about ¾ cup has been incorporated and the mixture is silky and lump-free.
In a small saucepan over low heat, combine the remaining milk and sugar. Stir until the sugar dissolves (do not boil). Remove from heat and whisk in the matcha paste until smooth and bright green.
Add the coconut cream, vanilla, and salt. Whisk to combine. Strain the mixture through a fine-mesh sieve into a large bowl or pitcher to remove any clumps.
Cover and refrigerate for at least 4 hours, or until very cold.
Whisk the chilled mixture, then pour it into the frozen ice cream maker bowl. Churn for 20–25 minutes, or until it reaches a soft-serve consistency.
Transfer to a loaf pan or airtight container. Cover tightly and freeze for 4–6 hours, or overnight, until firm.
Let the ice cream sit at room temperature for 10 minutes before scooping. For easier scooping, dip the scoop in hot water between each scoop.
Serve 1–2 scoops per bowl. For a Japanese-style presentation, dust lightly with extra sifted matcha powder and serve with a wooden spoon.