Step 1

Heat the oven to 400°F with a rack in the middle position

Step 2

Mist a 9-by-13-inch baking dish with cooking spray and set aside

Step 3

In a 12-inch skillet over medium, melt 4 tablespoons butter

Step 4

Add the potatoes and ½ teaspoon salt, then stir to coat

Step 5

Add ½ cup water, then distribute the potatoes evenly

Step 6

Cover and cook until a skewer inserted into the potatoes meet no resistance, 15 to 20 minutes, stirring once about halfway through

Step 7

Transfer the potatoes and any liquid in the pan to a large bowl, then use fork to mash to the consistency of chunky mashed potatoes; set aside

Step 8

Wipe out the skillet and set it over medium

Step 9

Add the oil, shallots and ¼ teaspoon salt

Step 10

Cook, stirring occasionally, until the shallots are softened but not browned, 5 to 6 minutes

Step 11

Add the beans and mushrooms, then increase the heat to medium-high

Step 12

Cook, stirring occasionally, until most of the liquid released by the mushrooms has evaporated and the beans are bright green but still crisp, about 5 minutes; the vegetables should not begin to brown

Step 13

Stir in the marjoram and cook until fragrant, about 30 seconds

Step 14

Transfer to the bowl with the potatoes and cool for about 10 minutes

Step 15

In a medium bowl, whisk the eggs, 2 ounces (1 cup) of Parmesan and ½ teaspoon each salt and pepper

Step 16

Add the egg mixture to the vegetable mixture and fold with a silicone spatula until combined

Step 17

Transfer to the prepared baking dish and spread evenly

Step 18

In a small bowl, combine the panko, melted butter and the remaining 1 ounce (½ cup) Parmesan, then stir until the panko is evenly moistened

Step 19

Sprinkle evenly over the vegetables

Step 20

Bake until golden brown and bubbling at the edges, about 30 minutes

Step 21

Cool for about 15 minutes before serving