Preheat the oven to 450 degrees and place a baking pan in the oven to get hot.
Meanwhile, shred the potatoes and shallots on the large end of a box grater. Place in cheesecloth or a towel and wring to get out as much water as you can. Place in a large bowl and add the green onions, egg, and a generous pinch of salt and pepper. Add in the flour, 1 Tbsp at a time until it starts to form into a loose, but large ball (you're looking for a "shaggy" dough like quality).
Remove the hot pan from the oven and spray with cooking spray. Working quickly, take a heaping spoonful of the potato mixture in your hand and flatten into a disc. Place on the hot baking pan; you should hear it sizzle. Repeat with remaining mixture (you may have to do this in batches depending upon how many you can get on a pan.
Bake for 5-10 minutes until golden brown, then flip (you can lightly spray the baking sheet again with cooking spray to ensure a golden brown crust) and bake for another 5-10 minutes until the potato pancakes are cooked through, crispy, and golden. Remove from the oven and sprinkle with salt and pepper, as needed.
To serve, let the potato pancakes cool slightly, then top each with a dollop of greek yogurt, followed by a generous portion of smoked salmon. Top with fresh chives or thinly sliced green onion and serve immediately.