Heat a small skillet, over medium heat, and melt butter with 2 tablespoons olive oil until bubbling.
Add leek and saute until it begins to soften, about 5 minutes; add thyme, season with salt and pepper, and cook about 1 minute more.
Meanwhile, whisk together egg whites and 2 tablespoons pecorino cheese; add to skillet and gently fold into leeks, to scramble, for 1 minute.
Transfer to oven and bake until the center is set (check by gently shaking skillet), about 7 minutes; transfer to a place and sprinkle with remaining pecorino cheese.
Toss the arugula and mizuna with the remaining olive oil and a healthy squeeze of lemon juice; season with salt and pepper, then pile on the frittata and serve.