In a medium size saucepan, melt 3 Tbsp of the butter over medium heat. Add flour and cook, stirring for 1 to 2 minutes without browning. Gradually whisk in milk and broth and cook, stirring constantly until smooth and thickened. Remove from heat, let cool 5 minutes
In a large bowl, combine chicken, 1 cup of the bread crumbs, parsley, salt and eggs. Mix well. Pour in sauce, blend and cover. Chill 2 hours, until set
Preheat oven to 350. Combine Parmesan cheese and remaining 1/4 cup bread crumbs in a shallow dish. Shape chicken mixture into 2 1/2-3 inch balls then roll into ovals (make 8). Roll croquettes in bread crumb mixture.
Arrange croquettes in a greased 12x8x2 inch baking dish. Melt remaining 2 Tbsp butter and drizzle over croquettes. Bake 20 minutes, until golden brown. **If using regular butter, melt remaining 1 Tbsp and brush on top of croquettes