Preheat your oven to 375°F and line a baking sheet with parchment paper. Finely dice the jalapeños into 1/8-inch pieces for mixing into the dough, and cut 24 jalapeño slices into consistent 1/4-inch rounds for topping—keeping them uniform ensures even cooking on each bagel. Freshly shred your cheddar cheese if you haven't already, as pre-shredded cheese contains anti-caking agents that prevent optimal melting. Crack your egg into a small bowl and whisk it lightly with a splash of water to create an egg wash.
In a large mixing bowl, whisk together the flour, baking powder, salt, garlic powder, and onion powder until evenly distributed. Add the finely diced jalapeños and freshly shredded cheddar, tossing gently to coat them in the dry mixture so they're distributed throughout. Pour in the Greek yogurt and stir with a wooden spoon or your hands until a shaggy dough just comes together—the Greek yogurt's thickness creates a denser, more bagel-like texture than regular yogurt. I like using FAGE brand specifically because the lower moisture content means less flour is needed and the bagels stay tender rather than dense.
Turn the dough out onto a lightly floured surface and gently knead it 2-3 times to bring it together—don't overwork it or the bagels will become tough. Divide the dough into 8 equal pieces using a bench scraper or knife, then roll each piece into a smooth ball. Using your thumb or index finger, push through the center of each ball to create a hole, then gently stretch and widen the hole to about 1.5 inches in diameter. The hole should go all the way through but not so large that it distorts the bagel's shape.
Place the shaped bagels on your prepared baking sheet and let them rest for 5-10 minutes at room temperature—this brief rest allows the gluten to relax slightly, preventing the bagels from shrinking in the oven. Brush each bagel generously with the egg wash from Step 1, making sure to coat the tops evenly. I like to use a pastry brush for even coverage, which gives the bagels a beautiful golden exterior. Top each bagel with a small pinch of the remaining shredded cheddar (about 1 teaspoon per bagel) and arrange 3 jalapeño slices on top, pressing them gently into the dough so they don't slide off during baking.
Place the baking sheet in your preheated 375°F oven and bake for 12-15 minutes, until the bagels are golden brown on top and cooked through. The jalapeño slices should be slightly darkened at the edges, and you should see cheese melting around them. Start checking at 12 minutes, as oven temperatures vary—you're looking for a light golden color rather than deep brown.
Remove the baking sheet from the oven and let the bagels cool on the sheet for 2-3 minutes, then transfer them to a wire cooling rack for about 10 minutes. This allows them to set and firm up slightly without becoming hard. Serve warm or at room temperature—they're delicious fresh from the oven with cream cheese, or sliced and toasted the next day.