Heat 2 tablespoons of the olive oil in a small saucepan over low until shimmering, 30 seconds to 1 minute. Add shallots and anchovies, and cook, stirring constantly, until shallots have softened and anchovies fall apart and dissolve, 2 to 3 minutes. Stir in crushed red pepper. Add vinegar, and cook, stirring often, until mixture has reduced slightly, about 1 minute. Remove from heat. Whisk in remaining 9 tablespoons oil.
Arrange tomato wedges on a platter, and top with warm vinaigrette. Sprinkle with parsley, and serve immediately.