Preheat oven to 400 degrees F. Grease 6 ramekins with butter and line the bottom of each with a buttered circle of parchment paper. Place the ramekins on a baking sheet.
In a double boiler or microwave in 20 second increments, melt the chocolate chips and butter until smooth. Set aside and allow to cool for 15 minutes.
In a large bowl, beat together the eggs and sugar until pale. Mix in the flour until smooth. Slowly fold in the cooled chocolate until combined.
Pour enough of the batter into each prepared ramekin to just cover the bottom. Add about 1 tablespoon of the chilled Matcha White Chocolate Ganache to the center of each ramekin over the chocolate batter, being careful to not allow it to go along the edges or bottom. Top with additional chocolate batter until the ramekins are 3/4 full, making sure it fully encloses the ganache.
Bake in preheated oven just until the tops are barely set but still wobbly in center, about 13 minutes- start checking at 10 minutes. Allow to cool for 15 minutes before inverting onto serving plates.
Serve immediately with a dusting of additional matcha, matcha or vanilla ice cream, whipped cream, and fresh berries.