Heat broiler. To make crostini: Arrange baguette slices on a baking sheet in a single layer. Broil for 1 1/2 minutes (the broiling time varies from oven to oven so watch carefully as bread darkens). Turn over slices, and toast until golden, about 1 minute more. Transfer to a rack to cool.
Rub crostini with tomato halves to infuse them with flavor and juices; discard tomatos. Drizzle crostini with olive oil. Top each crostini with a slice of ham. Brush with olive oil. Arrange on a serving platter, and sprinkle with parsley.