Heat the olive oil in a large, heavy pot over medium heat. Add the smashed garlic and cook for 1 minute. Add the stock and lemon halves and bring to a simmer.
Add the mussels, cover, and steam for 4 to 6 minutes, until the shells open. Discard any that stay closed. Remove the mussels from their shells.
While the mussels steam, heat a splash of olive oil in a skillet. Add the chard and garlic and cook for 3 to 4 minutes, until wilted. Squeeze out excess liquid.
Preheat the broiler. Combine the panko, melted butter, parsley, chives, garlic, and salt in a small bowl.
Arrange the flatbreads on a baking sheet. Top with the sautéed chard, cheese, and shelled mussels, then scatter the herb crumb mixture evenly over the top.
Broil for 2 to 3 minutes, watching closely, until the crumbs are golden and the cheese has melted.
Serve immediately with lemon wedges.