In a medium pot, bring potato shred to a boil in salted water; cook 10 minutes. Drain and cool completely. Meanwhile, combine cheese, Dijon, yogurt, and scallions in a large bowl.
Fold potatoes, broccoli, eggs, 2 Tsp. salt, and 1/2 tsp. pepper into cheese mixture. Cover with plastic; refrigerate at least 2 hours and up to 1 day.
Preheat oven to 400 degrees with a rack in top third. In a large oven-proof skillet, cook bacon over medium-high until crisp, about 8 minutes; transfer to paper towels to drain.
Add butter to skillet; when it foams, add potato mixture. Press to form and even layer and cook, scraping sides with a spatula to prevent burning, until it starts to set, about 8 minutes.
scraping sides with a spatula to prevent burning, until it starts to set, about 8 minutes.Transfer to oven; bake until golden, 22 to 25 minutes. Let cool slightly.
Crumble bacon on top and serve, with sliced scallions and yogurt.
