Combine warm water and yeast in a small bowl, set aside for 5 minutes.
Combine apple juice, applesauce, sugar, egg replacer, salt, oil and cinnamon in the bowl of an electric mixer with a paddle attachment. Mix until well combined.
Slowly add pizza crust mix until a soft dough forms – you will not use all of the mix. Place dough onto a surface coated with pizza crust mix. Knead until dough is soft but not sticky.
Roll dough to 1/4-inch thickness and cut into squares. Set aside at room temperature for 20 minutes.
Pour oil into a deep-sided pot until 2 inches in depth, heat over medium heat to 350ºF.
Lightly press beignets to slightly flatten.
Add a few beignets to oil and fry until golden brown on both sides turning once.
Remove from oil and place on a baking sheet lined with paper towels. Repeat with remaining beignets.
Dust with a generous amount of confectioners’ sugar before serving.