Peel the apple, then cut the sides away from the core. Chop into very small pieces.

In a pan over high heat, cook the apples with ground cinnamon, ground nutmeg, vanilla extract, organic brown sugar, and water for 15 minutes.

Reduce the heat to medium-low and cook for another 15 minutes, until the apples soften (about 30 minutes total).

If using active dry yeast, activate it in warm non-dairy milk. If using instant yeast, add it directly to the dry ingredients.

In a large bowl, combine flour, salt, and sugar.

Add melted vegan butter and the milk/yeast mixture. Mix with a spoon or spatula until a shaggy dough forms.

Knead for 5 minutes, until smooth.

Roll out the dough on a lightly floured surface into a rectangle about 12 x 15 inches and ¼ inch thick.

Spread softened vegan butter evenly over the dough.

Sprinkle with brown sugar, then ground cinnamon.

Distribute the cooked apples evenly on top.

Starting from a long side, roll the dough tightly into a log.

Slice the log in half, then cut each half in half, and finally cut each section into thirds, giving 6 rolls per log.

Place rolls in a 9 x 12-inch baking dish.

Cover and let rise for 1 hour (a turned-off oven is a good spot).

With 15 minutes left in rise time, preheat the oven to 350°F (176°C). If proofing in the oven, remove rolls before preheating.

Bake for 30–35 minutes, until golden brown.

In a stand mixer (with paddle attachment) or with a hand mixer, beat vegan butter and vegan cream cheese for 1 minute, until light and fluffy.

Add powdered sugar, brown sugar, and vanilla extract.

Beat on high speed for 3–5 minutes, until pale and creamy.

Let rolls cool for 30 minutes.

Spread frosting on top, then serve and enjoy.