Cook pasta according to package directions until al dente. Drain pasta and rinse with cold water; drain well.
Place 4 tablespoons melted butter in a large cooking pot over medium heat. Add garlic and chopped shallots; cook until shallots begin to become softened and clear. Whisk in flour and cook for one minute. Increase heat to medium high and add the milk. Bring to a boil, whisking frequently. Reduce heat to medium low and simmer until sauce is smooth and thickened. Remove from heat, and whisk in cheeses until melted. Add Dijon mustard, chives, cayenne pepper, and 1/4 teaspoon each of the salt and pepper. Fold in lobster and pasta; stir until thoroughly mixed. Set aside until you’re ready to fill filo cups.
Preheat oven to 350°F. Set aside 2 tablespoons melted butter to lightly brush inside of twelve 4×2-inch ramekins (8 ounce capacity). Reserve remaining butter to brush filo dough cups.
On a work surface, lightly brush 8 filo dough layers with butter as you overlap them into an 18×14-inch rectangle (or use 18×14-inch ready-made filo, which can be hard to find). Cut the rectangle into six square-ish pieces using a large, sharp chef’s knife. Press filo squares into ramekins, leaving corners to stick up over tops. Repeat process with remaining 8 sheets of filo dough. Brush insides of filo cups with melted butter, and spoon in lobster and pasta mixture into each one, filling just to top of ramekins.
In a saucepan over medium heat, lightly toast panko until golden brown, stirring frequently. Add remaining 2 tablespoons of melted butter and remaining 1/4 teaspoon each salt and pepper, stirring until thoroughly mixed. Remove from heat and let panko mixture cool for about 2 minutes. Sprinkle crumbs evenly over each filled filo cup. Transfer the ramekins to a baking sheet and bake for 20-30 minutes or until filo is golden brown and the sauce bubbles. Let the cups stand at least 5 minutes before serving.