Preheat your broiler.
Arrange the four flatbreads on an unheated broiler pan rack.
Layer the sliced tomatoes over each flatbread.
Season generously with salt and freshly ground black pepper.
Thinly slice the chilled Camembert cheese and arrange the slices evenly over the tomatoes.
Place the pan 4 to 5 inches from the heat and broil for about 2 minutes, or just until the cheese begins to melt and get bubbly.
Carefully remove the pan, sprinkle the chopped walnuts over the melted cheese, and return to the broiler for 1 more minute until the walnuts are lightly toasted.
Remove from the broiler, garnish with snipped fresh chives, and serve immediately.
Chilling the Camembert for at least 30 minutes before you begin is key. A firm, cold cheese is significantly easier to slice thinly and evenly.