Place water, sugar, and yeast in the bowl of a standing mixture and allow to sit until bubbly, about 5 minutes.
With a dough hook, mix in the butter, remaining sugar, salt and egg, then slowly pour in the warm milk. Add 3 cups of the flour. Once the flour has been incorporated, add in additional flour until the dough is tacky but not overly sticky.
Once the flour is incorporated, knead on low speed for 3 minutes then cover and let rise until doubled, about one hour.
Once doubled, punch down the dough and place on a lightly floured surface. Roll into a large rectangle (about 12-inches x 8-inches).
Cut into small rectangles (3-inches x 1-inch). Place on parchment-lined baking sheets (6 donuts per sheet). Cover and let rise until double, around 30 minutes.
Pour vegetable oil, 3-inches deep, into a pot. Heat oil to 350 degrees (F) then place 3 donuts into the hot oil and fry until golden brown. Flip over and fry until browned. Remove and allow to cool on paper towel-lined wire racks. Repeat with remaining donuts. Cool completely before filling.
While the dough is rising, place the instant pudding into a bowl and whisk the cold milk until smooth, about 2 minutes. Fold in the Cool Whip. Refrigerate until the donuts have cooled completely.
Place cream filling into a piping bag fitted with a small round tip (or in a ziplock bag with the corner slightly snipped). Poke a hole in the short end of a donut and pipe the filling into the donut. Repeat with remaining donuts and filling.
Place the confectioners' sugar into a medium-sized bowl. Whisk the maple syrup into the sugar along with the maple extract. Stir in 2 tablespoons milk. Add additional milk, 1 teaspoon at a time, until glaze reaches desired consistency.
Spread over the filled donuts and serve.
Best served right away. You may store leftover donuts in the refrigerator, in an airtight container, for up to 2 days.