Cut the crab legs into 3-inch pieces with kitchen shears. Cut along one side of the shell on each piece so the meat can be easily removed after cooking.
Place the remaining ingredients by the stove. Toast 2 tablespoons pepper in a small skillet over medium-high heat until fragrant, about 2 minutes; remove from the heat.
Heat the vegetable oil and butter in a large Dutch oven over medium-high heat until sizzling (you can also set a roasting pan over two burners). Add the garlic, ginger, scallions and jalapenos; sprinkle with the sugar and cook, stirring, until the mixture is fragrant, about 1 minute.
Add the crab pieces, oyster sauce and soy sauce. Cook, tossing, until heated through, about 5 minutes. Scatter the toasted pepper on top and continue to cook, tossing, about 1 more minute. Transfer the crab and sauce to a bowl. Serve with rice.