In a large bowl, whisk together the gluten-free flour, cocoa powder, salt, and baking powder. Set aside.
In the bowl of a stand mixer or a large bowl with an electric hand mixer, beat together vegan butter and light brown sugar until fluffy, about 3 minutes. Add the vanilla and beat again. Slowly add the dairy-free milk while continuing to beat.
Add half of the dry ingredients, beat again, and scrape the bowl with a silicone spatula before adding the other half and beating again. Once the mixture comes together, cover the bowl and let it rest for 30 minutes.
Preheat the oven to 350°F (175°C). Grease and line a half-sheet baking pan (13x18 inch) with parchment paper. Spread the rested cookie base mixture evenly over the parchment paper and bake for 10-12 minutes. Let it cool completely before letting it chill in the freezer while preparing the ice cream.
In a large bowl, beat the chilled oat whipping cream for 5 minutes. Add the sweetened condensed oat milk, vanilla, and beat until smooth. Let it chill in the freezer for 1 hour, until it thickens to the texture of softened ice cream.
Take the cookie base out of the freezer, and cut it in half so it creates two 9x13 inch rectangles. Evenly spread the ice cream base on one of the cookie layers. Top with the second cookie layer and wrap the large ice cream sandwich with plastic wrap and keep it in the freezer until completely frozen, about 6 hours or overnight. Take it out of the freezer once frozen, take the wrap off, and cut it into ---- pieces. Wrap each ice cream sandwich with plastic wrap and store in an airtight bag or container in the freezer until ready to serve.