For the frittata: Preheat the oven to 350 degrees F.
Whisk the eggs in a bowl with the cheese, 1/4 teaspoon salt and a few grinds of pepper.
Melt the butter in a 10-inch ovenproof nonstick skillet over medium heat. Add the greens and cook, stirring occasionally, until hot. Spread the greens in a single layer, then add the egg mixture. Scoop small spoonfuls of the pumpkins all around the egg. Cook the frittata until the eggs are set around the edge, about 3 minutes.
Transfer the skillet to the oven and bake until just set, 10 to 12 minutes. Let cool in the skillet for 5 minutes then invert onto a plate to serve.
For the cheesy bread: Heat a grill pan over medium heat. Rub the bread on both sides with the garlic. Brush the grill pan with olive oil and place the bread on top. Grill a few minutes on one side until you have grill marks but the bread is still a bit soft. Flip and top with the cheese. Cover with a metal bowl until the cheese is melted. (You can also do this under a broiler for a minute.) Top with the chives and serve with the frittata.