In the bowl of a stand mixer add 110F water (120 ml) and the granulated sugar (4 1/2 tsp). Stir to combine and slightly dissolve the sugar. Add the active dry yeast (2 1/4 tsp), stir quickly and set aside for 5-10 minutes to bloom.
Once the yeast and sugar mixture becomes foamy and bubbly, add the bread flour (500 g) and salt{1.5%tsp} to the bowl and mix using the dough hook attachment on low. Slowly begin to add the remaining 110F water (180 ml).
Once the dough has begun to come together, add the minced jalapeño (3 tbsp). Add 1-2 teaspoons of additional flour if needed as the jalapeños may release a little liquid. Allow the mixer to knead the dough for 10-12 minutes. The dough should be smooth (shaggy dough is too dry and sticky dough is too wet).
Remove the dough from the bowl, drizzle the bowl with the olive oil (some) and brush up the sides with a paper towel to coat the bowl. Return the dough to the bowl, cover with a damp kitchen towel and store in a warm place for 2 hours or until the dough has doubled in size.
After two hours, punch the dough down, cover and rest an additional 10 minutes.
Remove the dough from the bowl to a floured surface. Knead the dough for 2-3 minutes to return the dough to a smooth ball.
Using a sharp knife, divide the dough into 8 pieces. Pressing the dough between your palm and the floured counter, work in a circular motion to form a small ball. Punch your thumbs through the center and work in a circular motion to smooth the bagel shape.
Place the formed bagels on a parchment-lined baking sheet and cover with a damp kitchen towel for 10 minutes.
Preheat the oven to 425°F. Fill a large pot with water and bring to a boil.
Working 1-2 bagels at a time (depending on the space in your pot), add the bagels to the boiling water. Boil on each side for 1 minute, flip and continue to boil for an additional minute on the other side. Remove the boiled bagel from the water and place on a separate piece of parchment paper on the counter to slightly cool. Once all the bagels have been boiled and slightly cooled, move to the dry parchment-lined baking sheet.
Brush the bagels with whisked egg (1 ) wash and generously sprinkle each bagel with the cheddar cheese (1/2 cup) and top with slices of jalapeño (1 ).
Bake for 18-20 minutes until golden. Remove from the oven and cool for 5 minutes before slicing and devouring!