Preheat an non-stick electric griddle to 375 degrees. In a mixing bowl, whisk together flour, baking powder and salt. In a large mixing bowl, whisk together milk, eggs, 2 Tbsp vegetable oil, applesauce and granulated sugar until well blended. Add in dry ingredients and mix until combine (batter should be slightly lumpy, don't over-mix).
Pour half of the batter into a sandwich size ziploc bag and seal bag (I tried pouring all of it into a large ziploc and just found it was easier to work in two smaller batches). Brush preheated griddle generously with vegetable oil (I used a silicone baster and brushed the areas where the pancake batter would be poured. The vegetable oil is an important part of the "fried" doughnut flavor so that's why I stated "generously").
Cut about a 1 inch corner off the ziploc bag (while holding it with the tip pointing upward so the batter doesn't pour right out), then carefully pipe doughnut shapes onto oiled griddle*.
Cook pancake until golden on bottom, then lift pancake with a spatula and brush griddle again with vegetable oil then carefully flip to opposite side. Cook opposite side until golden. Repeat process with remaining batter. Serve Doughnut Pancakes warm, with Doughnut Glaze Syrup and sprinkles of course.
Doughnut Glaze Syrup
Melt butter in a medium saucepan over medium heat. Once butter has melted, stir in powdered sugar, salt and milk. Whisk until sugar has dissolved completely then stir in baking soda and whisk for about 30 seconds until frothy. Remove from heat and stir in vanilla. Serve warm over Doughnut Pancakes. Store in refrigerator up to one week.
Notes
*Note: the first pancake will probably be a practice pancake, the second should look better once you get the feel for it. The batter will spread slightly as it cooks so keep that in mind when judging how large you keep the hole in the center of the circle.
Also, after piping each pancake, return bag with the cut opening facing upright so batter doesn't continue to pour out. If you find it too difficult to get the shape you want you could just ladle (and slightly spread the batter so the centers aren't thicker) onto the griddle and do normal shaped pancakes then use a small circle cookie/fondant cutter and cut a circle through the center of the pancake after it's been cooked.