How to make Vegan Flatbread like Subway's?

Hello Vegans, I’ve been vegan since the beginning of the year (and was a long time ago).
Typically I am raw, but sometimes I like a massive assortment of greens as a sandwich.

The flatbread at subway is somewhat gooey, even after being toasted, I think the texture is perfect. My question, how could I accomplish making this? There are a ton of vegan flatbread recopies out there but its hard to tell which will have the sort of texture I am seeking. Essentially I want to finally divorce Subway and their $6 sandwiches for a gluten-free alternative with higher nutritional (organic/romaine/etc) value.

I found this recipe for Subway flatbread … _Flatbread
You could try adjusting this recipe by using vegan milk+butter, I’m not sure if that would yield the same texture or not but it’s an idea