Place the grated zucchini in a strainer and squeeze out as much of the liquid as possible. Whisk egg in a medium bowl, then add zucchini and scallions.
Next, add the dry ingredients and fold together using a spatula until little dry spots remain. Allow to sit for 10 minutes.
Place a large skillet over medium-high heat. Add 1/3 cup olive oil and heat until the oil begins to ripple. Add 1⁄4 cup of the batter per latke, arranging about 6 in the pan at a time, making sure there is enough space to turn them.
Cook for 3-4 minutes on each side, or until golden brown. Transfer to a parchment-lined baking sheet or plate. Continue with the remaining batter.
Serve with a dollop of crème fraîche and caviar on each.