Preheat the oven to 375 degrees. Line a baking sheet with parchment paper.
Place the baguette slices on the lined baking sheet. Bake until starting to crisp but not totally toasted, about 5 minutes.
In a mixing bowl, stir together the cheeses, parsley, lemon zest and anchovy paste. Spread 1 tablespoon of the mixture onto the center of each baguette slice, being sure to leave a border of clean bread surrounding the cheese (it will spread as it melts in the oven). Place an artichoke heart in the center of each and set back on the baking sheet. Sprinkle about 1/2 teaspoon of grated Parmesan over each artichoke heart.
Bake until the Parmesan is melted, about 10 minutes. Serve warm.