1. In a small sauce pot, heat 1 tbsp of the olive oil over low heat until shimmering. Add shallot and anchovies and cook, stirring, until shallot has softened and anchovies fall apart and dissolve in oil, 2 to 3 minutes. Stir in red pepper flakes. Add vinegar and cook, stirring, until it has reduced slightly, about 1 minute. Whisk in remaining 4 tbsp olive oil.
2. Arrange tomato wedges on a platter and spoon warm vinaigrette over them. Garnish with parsley leaves and serve immediately.