To make the dough by bread machine:
Add the milk, water, flour, malt powder or sugar, and yeast to the pan of your bread machine in the order recommended by the manufacturer. Select the "Dough" or "Dough Only" cycle and hit start. Allow the cycle to complete.
To form pretzel bites:
Line two 11-by-13-inch baking sheets with silicon or teflon pan liners. (You can use parchment, but you will need to grease it generously to prevent it from sticking.) Set next to your work area.
Turn the dough out onto a very lightly floured surface. Use a bench knife to cut the dough into four pieces. Keep three pieces of dough covered with a tea towel while working with the first. Roll the piece like play-dough until you have a snake of dough about the circumference of two thumbs squashed together. Use your bench knife to cut the dough snake into 6 equally-sized pieces. Press each piece into an oval that is about 3-4 inches across. Put 1½ teaspoons each of the ham and cheddar into the center. Bring the dough up together from the sides toward the center and pinch together firmly to seal the dough. Pinch the ends so that the cheese and ham are sealed into the dough.
Transfer the sealed, stuffed dough, seam-side down, onto the lined baking sheets, being sure to leave generous amounts of room between pieces and rows. They will expand both as they rise and again as they boil and bake.
To cook the pretzels:
Preheat oven to 400°.
Bring 2 quarts of water to a boil in a stainless steel or other non-reactive pan (enameled cast-iron, tempered glass, etc.) When water boils, add the baking soda. Gently lift the pretzel dough pieces one at a time into the boiling water. (You can boil more than one at a time, but be sure not to crowd the the pan as they will expand as they boil. Let simmer for about 45 seconds, flip the pieces and simmer for another 45 seconds-1 minute. Use a slotted spoon to drain and return each piece to its place on the pan. Continue until all pieces have been boiled and returned to the pan.