Prepare or warm the marinara sauce and set aside.
In a large bowl, whisk together the flour, 1/4 teaspoon Kosher salt, and 1/4 teaspoon black pepper.
In a separate bowl, whisk the 4 eggs, 3/4 cup whole milk, and 3/4 cup heavy cream until combined.
Gradually add half of the egg mixture into the flour mixture while whisking vigorously until smooth, then whisk in the remaining egg mixture until completely smooth.
Cover the batter and refrigerate for at least 30 minutes (or up to 12 hours).
Strain the chilled batter through a fine-mesh sieve into a bowl and stir in 2 tablespoons melted unsalted butter.
Heat an 8–9 inch non-stick skillet over medium and lightly oil it. Pour about 1/4 cup batter into the pan and swirl to form a thin crêpe.
Cook the crêpe 1–3 minutes until set and lightly browned on the bottom, flip carefully, and cook another minute. Transfer to a plate and separate crêpes with parchment; repeat until batter is used. Let cool completely.
In a large bowl, combine ricotta, chopped fresh mozzarella, shredded smoked mozzarella, 3 tablespoons grated Pecorino Romano, 1/2 teaspoon Kosher salt, and 1/4 teaspoon black pepper.
Stir in 2 tablespoons chopped basil and 1 tablespoon chopped parsley, then gently fold in the lightly beaten egg until smooth. Cover and refrigerate 30 minutes or overnight.
Preheat the oven to 375°F (190°C). Spread 1–2 cups marinara across the bottom of a 9x13 inch baking dish.
Working one crêpe at a time, place about 3 tablespoons filling on the lower third of a crêpe, roll into a tube, and arrange seam-side down in the baking dish on top of the marinara. Repeat with remaining crêpes and filling.
Smear the softened 2 tablespoons butter over the tops of the rolled crêpes and sprinkle a few tablespoons of the remaining grated Pecorino Romano over them.
Bake on the middle rack 12–15 minutes until cheese is melted and bubbly; optionally broil briefly to brown edges, watching carefully to avoid burning.
Warm any remaining marinara while baking. Remove the manicotti from the oven, let rest 10 minutes, garnish with 2 tablespoons chopped parsley, and serve with warmed marinara.
