I do bagels Mikey's way. Bagel flat on the board, fingers flat on top, and slice through parallel to the board. I got a new Canadian Maple chopping board for Christmas!
For peppers, there are two ways I was taught. Cut the three lobes off the stalk leaving the stalk and seeds behind. I cut the pepper in half through the stalk top to bottom, then I cut around the halved stalk taking the seeds.
For the chewy bagel people, aren't they supposed to be toasted? We always do.