Melt butter in a large sauté pan over medium-low heat. Add two tablespoons oil. Add next 8 ingredients and cook until the vegetables are soft, approximately 15 to 20 minutes. Cool to room temperature. In a large bowl, break the lump crabmeat into small pieces and toss with the bread crumbs, mayonnaise, mustard, and eggs. Add the cooked mixture and mix well. Cover and chill in the refrigerator for 30 minutes. Shape into bite-sized crab cakes. Heat the butter and 1/4 cup olive oil over medium heat in a large sauté pan. Add the crab cakes and fry for four to five minutes on each side, until browned. Drain on paper towels; keep warm in a 250°F oven until ready to serve.
