If making homemade oat milk, combine 720mL water, 54g rolled oats, and 40g nuts or seeds in a blender. Blend in high speed for 1 minute. Pass the mixture through a cheesecloth set over a fine mesh strainer or a nut milk bag. Yields approximately 650g oat milk (a tad more than called for in the ice cream base), and can be made up to 3 days in advance and stored in the refrigerator until use.
Disperse the stabilizer. In a medium bowl, whisk together dry ingredients: 120g dextrose, 75g sucrose, 1.5g salt, 20g inulin powder, 1.5g CMC, 0.5g guar gum, and 1g soy lecithin.
Blend the base. In a blender or large container with an immersion blender, combine 600g plant milk, 35g liquid oil, 90g refined coconut oil, and dry ingredient mix. Blend on high for 30 seconds.
Age the base. Transfer the blended mix to an airtight container and refrigerate overnight or for at least 8 hours.
Churn the ice cream. Spin the mix in an ice cream machine according to machine directions, until soft serve consistency. Transfer to a container and freeze for at least 4 hours to fully firm up.