In a large pot over medium heat, stir together the beer, Velveeta, sugar, salt, and butter until just melted.
Remove from the heat and allow to cool until it's just warm - around 110 degrees. Too hot and it will kill the yeast, too cold and your bread won't rise! Stir occasionally as it's cooling to keep the cheese incorporated and to help speed up the cooling process.
In the bowl of your stand mixer fitted with the dough hook, combine 2 cups of the bread flour and the 2 packets of rapid rise yeast.
Pour the warm beer mixture into the flour and yeast and turn your mixer until low speed and gradually add the remaining flour until the dough is a shaggy and cleans the sides of the bowl.
Turn mixer to medium and knead dough for 5 minutes.
Pour the cubed cheddar cheese into the mixer and allow it to incorporate into the bread dough.
Remove the dough from the mixer and grab any stray cheese cubes from the bottom of your mixing bowl and poke them throughout the dough.
Place dough in a greased bowl and allow to rise in a warm place until doubled - about an hour, but sometimes a bit more.
Punch the dough down and separate into two equal balls.
Place one ball of dough on a floured surface and press into a rectangle shape about 10x6 inches.
Cut the dough into three long strips, leaving 1/2 inch intact at the top of the rectangle. Braid the dough and tuck the ends under.
Repeat with second ball of dough.
Spray two 8x4 loaf pans with cooking spray and place the loaves inside.
Return to a warm spot and let rise again, about 1/4 inch above the pan.
Bake for 350 degrees for 35-40 minutes, tenting the top with foil for the final 10-15 minutes of baking time.
Turn the loaves out onto a wire rack to cool.