In a mixing bowl, mix together the dry ingredients: the flour, yeast, sugar, and salt.
Make a well in the center of the dry ingredients and then add the warm water and the olive oil. Using a stand mixer fitted with a dough hook, knead everything together until the dough is smooth and elastic, approximately 4-6 minutes. If the dough is very sticky after 3 minutes, you can add up to half of a cup more of flour, in 2 tablespoon increments.
Cover with a clean dish towel or plastic wrap and let rest in a warm spot for 30 minutes to 1 hour until the dough has risen. (It might not quite double in size if you only let it rest for 30 minutes, but that is okay. We really just want a bit of elasticity so that we can shape the dough easily around the cream cheese.)
Line a baking sheet with parchment paper and set aside. Then turn the dough out onto a clean, unfloured surface. Roll into a log. Then divide into 16 portions of dough, 1.4 to 1.6 ounces each. Form each piece into a ball by rolling on the countertop with a cupped hand. They will be slightly larger than a golf ball. As you work with each piece through the next few steps, keep the dough that you’re not working with covered in plastic wrap.
At this point, preheat your oven to 375F. You should also prepare your poaching water by bringing a pot filled with 6-8 cups of water to a boil. Add in malt syrup or honey and give it a stir.
While you’re waiting for the pot to come to a boil, stuff the bagel bites with cream cheese. Start by cutting your block of cream cheese into 16 pieces.
Then, take a dough ball and flatten it. You can use a rolling pin, but I like to use the palm of my hand and then flatten the edge of the disc with my fingers, leaving the center a bit thicker so that the dough is evenly stretched around the cream cheese. Place a cube of cream cheese in the center of the disc. Then gently pull the edges of the dough up around the cream cheese to wrap it, pinching the dough tightly closed and then gently rolling it on the counter. Place it on the baking sheet and repeat until done.
By this time, your poaching water should be boiling. Gently lower 3-6 bagel bites into the pot at a time, or as many as fit comfortably. Boil for 30 seconds, flip, and boil for another 30 seconds. Transfer back to the parchment paper with a slotted spoon (I use a meshed strainer that we use for hot pot parties). And repeat until you have poached all of the bagel bites.
Brush the bagel bites with egg wash and sprinkle with everything but the bagel seasoning. I used ¼ to ⅓ of a teaspoon for each bite, but you don’t have to be super precise here. Alternatively, you can skip the egg wash and sprinkle with the everything bagel seasoning immediately as they come out of the poaching water.
Bake bagel bites for 25-27 minutes or until golden brown. Let cool for a few minutes because the cream cheese will be molten hot.