Steam fresh crabs for 10 minutes until bright red, cool, and carefully extract crab meat without shell fragments.
Melt butter in a saucepan over medium heat, add minced garlic, and sauté for 1-2 minutes until fragrant without burning.
In a mixing bowl, gently combine crab meat, melted garlic butter, lemon juice, parsley, chives, salt, and pepper.
Preheat oven to 375°F (190°C).
Arrange baguette slices on a baking sheet and brush both sides lightly with olive oil.
Toast baguette slices in the oven for 5-7 minutes until golden brown and crispy on edges.
Remove toasted bread from oven and spoon crab mixture generously onto each slice.
Optionally sprinkle grated Parmesan cheese over the crab mixture.
Return assembled toasts to oven for 5 minutes to meld flavors and melt cheese slightly.
Remove from oven, garnish with paprika if desired, and serve immediately.