In the bowl of a stand mixer, combine yeast, warm water, and honey; let it sit until bubbly, about 30 minutes.
In a large mixing bowl, combine flour, sea salt and Pepper Jack cheese; stir until well blended.
Add the dry ingredients to the yeast mixture.
With the dough hook attached, process on speed 2 for 5 minutes. Scrape the sides and bottom of bowl before increasing to speed to 3; knead for 5 minutes.
Increase the speed to 4 and process for another 5. If the dough is not smooth, add ¼ cup more flour and knead again for 5 minutes or until the dough forms a ball and bouncy.
Place the dough on a lightly floured work surface and with floured hands, stretch to form a rectangular shape. Add most of the jalapeño peppers and flip the dough over, kneading it. Add the remaining peppers, knead again and form a ball.
Place the dough in a greased bowl, swirling it to coat with oil.
Cover with a clean dish towel, and let it rise for 1 hour in a warm, draft-free area such as an oven (temperature off) or until it doubles in size.
Remove the dough from the bowl onto a floured work surface, sprinkle flour on top and knead it again.
Form a ball by pulling under and, using a bench scraper, separate the dough into 8 equal pieces before forming them into balls.
Roll each ball down to a 4-inch diameter. Make a hole with a 1 ½-inch cookie cutter or stick your thumb through the center. Reuse the holes by rolling another bagel and stick your thumb through the center - don’t use the cookie cutter.
Place bagels on a baking sheet lined with parchment paper, cover with a clean dish towel and proof for 20 minutes.
Preheat oven to 400ºF.
In a large shallow skillet filled with water and kosher salt, bring it to a boil.
Place bagel in the boiling water without crowding it and boil 1 minute per side.
Strain bagels on a wire rack until excess water drips off while boiling the others.
Transfer the bagels to a baking sheet lined with a silicone mat or parchment paper. Brush bagels with egg wash and top with sharp Cheddar cheese, covering the entire surface. Place several jalapeño slices over the cheese, pressing down gently to prevent them from falling off.
Transfer them to the preheated oven and bake for 25 to 30 minutes or until the sides and tops are golden, turning the baking sheet halfway through cooking.
Allow to cool on a wire rack for 10 minutes before serving.