Fry the chicken breasts in 1 tablespoon butter and the canola oil in a skillet over medium-high heat until done in the middle, about 8 minutes. Set aside.
To assemble the sandwiches, spread a generous amount of mustard on half of the bread slices. Spread a generous amount of ranch dressing on the other half. (Definitely be generous; when the sandwiches cook, these will turn into more of a "sauce.")
On the ranch-covered slices of bread, place a slice of cheese, a piece of chicken, 2 slices of bacon and a second slice of cheese. Top each with the mustard-covered slice of bread. Butter the outsides of the bread generously with the remaining 4 tablespoons butter, then grill in a panini maker. (If you do not have a panini maker, you can grill the sandwiches in a skillet, laying a heavy skillet on top of the sandwiches to press them together. Turn to grill the other side in the same way.)
Slice the sandwiches in half and gobble them down immediately.