Preheat broiler to high.
Lay cherry tomatoes and shallots in a baking sheet in an even layer. Broil for 12-15 minutes or until charred and tomatoes are softened. Let cool.
Preheat oven to 400 degrees. Line a baking sheet with parchment paper.
Lay prosciutto on prepared baking sheet and bake until crispy, about 7-8 minutes. Remove from oven and break prosciutto into small chunks. Set aside.
Combine tomatoes and shallots with thyme, salt, and red pepper flakes in a food processor. Puree until smooth. Add butter and mix until well combined.
Spread tomato butter on sliced bread and top with gruyere cheese. Transfer to a baking sheet and bake for 3-4 minutes or until cheese is melted.
Meanwhile, make scrambled eggs. Beat eggs in a large bowl and heat 1 tablespoon butter in a large saute pan over medium heat. Pour eggs and cook until desired degree of doneness. Season with salt and pepper and remove from heat.
Remove toast from the oven and top with scrambled eggs. Sprinkle crispy prosciutto on top followed by chopped chives. Serve immediately.