2ouncesgruyere cheeseshredded, about 1/2 cup (fontina or gouda would be great too!)
1ounceParmesan cheesefinely grated, about 1/4 cup
1(14-ounce) can artichoke heartsdrained, patted dry, and roughly chopped
1(4-ounce) can lump crab meatdrained
Place the oven rack in the upper third of the oven. Turn on the broiler to high. Line a baking sheet with parchment paper.
Cut the baguette into 1/4-inch slices (you should have about 24 total). Arrange in a single layer on the prepared baking sheet.
In a large bowl, stir together the Greek yogurt, 2 tablespoons parsley, lemon zest, lemon juice, garlic powder, salt, pepper, and cayenne. Stir in the gruyere and Parmesan, then gently fold in the artichokes and crab. Taste and adjust seasoning as desired.
Spoon 1 heaping tablespoon of the artichoke-crab mixture onto each baguette slice. Broil until the cheese begins to melt, about 3 minutes. Watch very carefully the entire time so that the toasts do not burn. Sprinkle with remaining 1 tablespoon fresh parsley. Serve warm or at room temperature.
Make-ahead tips: Crab mixture can be prepared and refrigerated 1 to 2 days in advance (1 is ideal but 2 is doable). Baguette can be sliced 1 day ahead and stored in an airtight container at room temperature. Top the toasts and broil shortly before serving.