Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
Toss chopped apples with 1 tablespoon brown sugar (12 grams) and cinnamon. Lay on the prepared baking sheet and scatter butter on top. Roast apples for 15 minutes, stirring halfway through. Remove from oven and let cool.
Reduce oven temperature to 325 degrees F.
Beat cream cheese with remaining ¼ cup brown sugar (50 grams) and vanilla extract until smooth. Fold in roasted apples until well combined. Scoop cream cheese filling into 1 heaping tablespoon balls and place on a lined baking sheet. You should have a total of 20 portions. Chill in the freezer until ready to use.
Prepare bagel bites dough. Combine active dry yeast with warm water and honey, gently stirring to combine. Let sit for 5 minutes or until yeast is activated and mixture is foamy.
Combine yeast mixture with bread flour, sugar, salt, and cinnamon in the bowl of a stand mixer. Knead dough for 7-8 minutes or until smooth. Transfer dough to a clean bowl, cover, and let rest for 45 minutes.
Punch down dough and divide into 20 portions. Roll each portion into a ball and flatten into a 4-inch circle. Place the cream cheese filling in the center and gather the edges to close the filling. Gently roll to shape into a circle and place on a lined baking sheet. Repeat with the remaining portions. Loosely cover with a clean kitchen towel and let rest for 20 minutes.
Line 2 baking sheets with parchment paper and spray with cooking spray.
Bring 2 quarts of water with 2 tablespoons of honey to a boil in a large pot over high heat. Gently add a few of the bagel bites into the water and boil for 15-20 minutes. Remove bagel bites with a slotted spoon and place on prepared baking sheets. Repeat with remaining bagel bites.
Add 2 tablespoons sugar with 1 ½ teaspoons cinnamon in a small bowl until well combined. Brush bagel bites with egg wash and sprinkle cinnamon sugar on top. Bake bagel bites for 25-30 minutes or until golden brown. Remove from oven and let cool slightly on a wire rack. Serve warm with extra cream cheese if desired.