On a floured surface roll out dough to a 10-inch circle. Transfer to a large lightly-greased cookie sheet.
In a saute pan melt butter. When it begins to foam add red peppers and onions and cook for 2 minutes. Add flour and cook, stirring, for 3 minutes. Add crawfish and cook for 2 minutes more. Remove from heat and fold in cheese and green onions. Season to taste with salt and cayenne.
Mound crawfish mixture in center of pastry circle, leaving a 2 to 3-inch border of pastry. Fold excess pastry up over filling, layering it over, but not completely covering filling. Work around circle, continuing to fold over previous fold, until it forms a rustic, freeform tart. Slide cookie sheet into oven and bake for 35 minutes.