Set aside a few onion rings. Dice the remainder of the onion and place into 6-quart sauce pan with milk, oil, salt and mashed potatoes. Turn on low heat and warm to 100º, exactly.
Place fresh yeast, warm water (105º) and oil into a large mixing bowl and whisk until yeast dissolves.
In a mixer bowl, combine flour, heated mixture and dissolved yeast in a mixer bowl. Mix on low speed using dough hook for 1 minute to incorporate the flour. Then mix on medium for 2 minutes until a ball has formed. Add more water or flour depending on temperature and humidity.
Remove the dough hook and allow bread to rise until it has doubled in size. Divide mixture into fourths and pat onto pre-oiled cookie sheets (two per sheet). Top the focaccia with a light coating of oil and other toppings of your choice (the reserved onion rings, sliced garlic, tomatoes, fresh herbs).
Let the dough rest for a second rising - approximately one hour. Bake at 350º for 10 minutes. Rotate and bake for an additional 10 minutes or until golden brown. Let rest five minutes before cutting. Serve warm with a dipping plate of olive oil topped with Parmesan cheese and ground black pepper.