Whisk together the starter, beer, and sugar in a large mixing bowl.
In another mixing bowl, whisk together the flour and salt. Then add this mixture to the wet mixture. Stir with a spoon until it comes together and then use your hands to finish mixing until a rough, stiff dough is formed. If the dough seems too dry, add more beer in half teaspoon increments until the dough comes together but is not sticky. The dough should be firm and dense.
Cover the bowl of dough with plastic wrap and let rest for about one hour. No need to be exact here.
Add mix ins: Remove the dough from the bowl and stretch it out into a large square/rectangle/circle shape (maybe around 12x12 or 12 inches in diameter or a little more) on a silicone mat or your counter. Don’t worry if the shape is not perfect. Pat your peppers/garlic dry again and then sprinkle them over the dough. Then sprinkle your 110g of shredded cheddar over the dough.
Roll up the dough: Roll the dough like you’re rolling up a cinnamon roll - or a yoga mat - grab one side and gently roll up so it looks like a log. Then take the bottom of the log and roll it up. Then form a ball. Place the dough ball back into the bowl and cover it with plastic wrap.
Rise: Let the dough rise overnight for 8-12 hours or until doubled in size. I live in Florida, my house is around 74 at night, and I let it sit out all night. In the morning, put the dough into the fridge. Leave the dough in the fridge for a few hours - I have left it all day while at work for nearly 12 hours and it was fine. You want to get the dough cold so it is easier to work with.
Shape: Weigh the dough. It should be around 1000g/1kg. Then divide that number by 8. That number will be the weight of each bagel dough ball. Don’t worry if one or two are smaller than the others-it’s ok, it won’t be enough to notice. Cut the dough into pieces (weigh each piece to match the number you previously calculated) and then roll each piece into a ball. Set them on a silicone mate lined baking sheet. You can also use parchment paper instead of a silicone mat. Let the dough rest uncovered for 12 minutes. I rest them for 12 minutes but you can rest them from 10-15.
After the dough has rested, shape the dough balls into bagels. Poke a hole in the middle of each dough ball with your index finger. Pick up the dough and work it to create the hole and the bagel shape. I like to but the bagel around my index finger and spin it a few times to help with shaping. Don’t worry if they don’t look perfect. They will puff up during the boil and baking processes. Place the shaped bagels on to the silicone mat or parchment lined baking sheet. Cover with a damp paper towel or teal towel and let rest for 17 minutes - that’s how long I rest them. You can rest them for 15-20 minutes. They will barely rise during this rest.
Boil: Add water and honey to a large pot and bring to a boil. Boil two bagels at a time for 30 seconds per side. I use my phone timer to track this. The bagels will puff up now! Use a slotted spoon or a fish spatula to add to, flip within, and remove the bagels from the water. Place them back onto the lined baking sheet. Repeat until all bagels are boiled.
Bake: Bake at 425 for 17 minutes. Then add the shredded cheese topping to the top of each bagel. Return to the oven and bake for 6 more minutes. Allow the bagels to cool on a wire rack.
Store in an airtight container or wrapped in plastic wrap/ziplock bags for 2-3 days. You can also wrap them well in plastic and then put them into freezer bags and freeze them.