Grease a baking sheet with a little oil. Cut the potatoes in half and place them, cut side down on the baking sheet. Bake at 400ºF for 40 minutes until the potatoes are very soft. Let the potatoes cool and then peel the skin from the potatoes and discard. Mash the peeled sweet potatoes with a fork and measure out 3 cups. (Reserve any remaining for another use.)
Combine the mashed sweet potatoes, shredded apples, whole-wheat flour and eggs in a bowl. Mix the ingredients well until a dough comes together, adding more flour if necessary to make the dough soft but pliable. Divide the dough into quarters and then cut each quarter in half. Roll the dough pieces into thin 16-inch logs. Twist 2 of the logs together and then cut the twisted log into 1- to 4-inch pieces, depending on what size treat you’d like for your pup. Alternately, form the log into any shape you want, hearts, circles, dog bones, your pup’s initials…get creative!