Preheat the oven to 375 F. Place a rimmed baking sheet in the oven to heat.
To make the pancakes: Steam the broccoli until tender but still crisp, about 3 to 5 minutes. While the broccoli cooks, saute the spinach in 1 tablespoon of the olive oil in a skillet until wilted, about 3 minutes, then remove from the heat and roughly chop.
In a large bowl, scramble the eggs, and then add the baking soda, flour, panko and Parmesan cheese; stir to combine. Add the broccoli, spinach and half the scallions. Mix to combine.
Remove the hot baking sheet from the oven and grease with the remaining 2 tablespoons olive oil. With an ice cream scoop, place pancakes evenly on the baking sheet. Gently press the top of each pancake to flatten. Bake for 10 minutes, then flip and bake for another 2 minutes, or until the centers of the pancakes are cooked through.
To make the poached eggs (start with about 8 minutes remaining on the pancakes): Boil the water in a large high-rimmed skillet. Once the water comes to a boil, crack each egg into its own ramekin. Add the white vinegar to the boiling water, reduce the heat to medium-low and drop each egg into the hot water. Cover the skillet and let the eggs cook for 3 minutes.
Remove the pancakes from the oven and serve 2 or 3 to a plate depending on their size. Top each plate with a poached egg and a sprinkle of the remaining scallions. Serve immediately.
Tip: If poaching all four eggs at once feels too daunting, try two at a time. Eggs cook quickly and this won’t greatly delay your meal.