Place potatoes in a large sauce pan or stock pot with water and 1 tsp salt. Bring to a boil and cook until soft, 15 to 20 minutes.
While the potatoes are cooking, place chopped onions and 1/2 tsp salt into a skillet with the vegetable oil and cook on low heat until the onions have softened, 5 to 7 minutes.
In a small saucepan, melt the butter, then add the half and half and 1 cup of the vegetable broth, keep warm.
Once the onions are done, place them into a food processor along with the garlic and the remaining vegetable broth. Chop until the onions are finely chopped.
Drain the potatoes, add the onions and the melted butter with the liquids. Use a hand mixer to mash them until they are smooth. Let the potatoes cool. (I put 4 inches of cold water in the sink and placed the pot into it for 15 minutes).
Add the eggs one at a time and mix them in. (Alternatively, you could use 4 to 6 ounces of softened cream cheese rather than the eggs. The eggs give the potatoes an airy lift while the cream cheese would not. Both would be equally good). Taste the potatoes and adjust salt and pepper seasoning.
Add the scallion greens and fold in with a spoon or spatula.
Spray cooking oil in a 3 quart casserole dish and add the mashed potatoes. Cover with plastic wrap and store in the refrigerator overnight.
Take the potatoes out of the refrigerator at least one hour before placing in the oven. Use a spoon or fork to make peaks, then place into a 350 degree oven for 45 minutes until the potatoes are warm and the peaks are starting to brown. (If you make this the same day, allow 30 to 35 minutes in the oven).