combine yeast, 1 t. brown sugar, and warm water in a lg. bowl. set aside

in another bowl stir remaining 2T. brown sugar and warm milk. add 2 1/2 c. flour and milk mixture to yeast mixture. stir until a soft dough forms. add remaining flour as needed.

knead dough on a floured surface to form a soft ball. transfer to an oiled bowl, cover with cling film, and let rise until doubled.

on a lightly floured surface cut dough into 4 pieces. roll 1 section into a 12 x 4 rectangle. with the long side facing you, spread with ham and cheese and roll jelly-roll style. cut into 12 pieces and transfer to a baking sheet. repeat with the remaining 3 portions of dough.

let the dough pieces rest for 30 minutes. preheat oven to 400°F. bring the 6 cups of water to boil, add baking soda, reduce heat to simmer, and cook bagel bites in small batches for 20 seconds. transfer back to the baking sheet and bake in the oven until brown, 15 minutes approximately.

remove from oven, brush with butter, and sprinkle with salt.