Halve and peel onions. Slice halves into thin strips. Place biscuit mix and shredded Asiago in a medium mixing bowl. Measure out 3/4 cup water. Add half the water to biscuit mix and mix with a wooden spoon until a sticky dough that just holds together forms. Add more water 1 Tbsp. at a time if too crumbly.

Use a 1/4 cup measure or large spoon and divide biscuit mixture on prepared baking sheet into 12-14 mounds, slightly smaller than ping pong balls. Brush tops lightly with olive oil and bake until golden brown, 14-16 minutes. While biscuits bake, start apple-cinnamon butter.

In a small pot, combine applesauce and cinnamon. Place over medium heat and bring to a simmer. Reduce heat to medium-low and cook, stirring occasionally, until reduced to a thick spread, 18-20 minutes. While apple-cinnamon butter simmers, start onion jam.

Heat 1 tsp. olive oil in a medium non-stick pan over medium heat. Add onions to hot pan and cover. Cook, stirring occasionally, until onions are fully softened, 10-12 minutes. Uncover and add sugar and balsamic vinegar. Cook, stirring often, until liquid is mostly reduced and onions are sticky and jam-like, 6-8 minutes. Season with 1/4 tsp. salt, stir, and set aside.

In a small bowl, stir softened butter and cherry jam with a whisk or wooden spoon until combined.

Serve biscuits in a bowl or on a plate with apple-cinnamon butter, onion jam, and cherry butter on side.