Preheat the oven to 180°C or an air fryer to 160°C on the bake setting. Grease a 2lb loaf tin (approx. 900g).
Add the self-raising flour, icing sugar and salt to a large mixing bowl and stir to combine.
Add the cold vegan butter and use your fingertips to rub it into the flour mixture until it resembles damp sand or breadcrumbs.
Add the coffee and oat milk and stir until the dough comes together into a soft clump. Lightly dust the dough with flour and knead for 2–3 minutes, until it holds its shape.
Dust your work surface with flour and roll the dough out into a rectangle, approximately 45cm × 30cm. The dough should be soft but easy to handle.
Melt the vegan butter for the filling. In a separate bowl, mix together the brown sugar, cinnamon and ground coffee.
Spread the melted butter evenly over the dough, right to the edges. Sprinkle over the coffee cinnamon sugar.
Starting from the long side of the rectangle, tightly roll the dough into a log.
Cut the log in half, then cut each half in half again, and repeat once more until you have 16 pieces. Place the swirls cut-side up in the greased loaf tin.
Bake in the oven for 25 minutes, or air fry for 18–20 minutes, until golden and cooked through.
While the swirls are baking, make the icing. Add the cream cheese, icing sugar, vanilla and oat milk to a bowl. Mix with a fork until smooth and creamy.
Remove the swirls from the oven or air fryer and drizzle over the cream cheese icing. Finish with a dusting of cacao powder.