For the filling: Melt the butter in a medium saute pan over medium heat. Add the leeks and saute until wilted and very soft, 4 to 5 minutes. Add the garlic and saute until fragrant, about 1 minute. Season with salt and pepper, and then transfer to a medium bowl.
Stir in the soft cheese until it melts and the mixture becomes creamy. Stir in the Parmesan and parsley. Season with red pepper flakes if using. Set aside (you can scoop the filling later or pipe it by transferring the filling to a disposable piping bag with 1/2-inch opening cut from the tip).
For the cigars: Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Open the phyllo dough and unfurl it. With one of the shorter sides facing you, cut the dough in half lengthwise (you're aiming for rectangles about 7-by-18-inches long, but exact size may vary based on brand of dough). Cover the dough with a lightly damp clean kitchen towel so it doesn't dry out while you assemble the cigars.
Make a cigar by placing one sheet of cut phyllo on your work surface with one of the shorter sides facing you. Brush the dough all over (but lightly) with the melted butter and top with another piece of dough. Continue this process until you've layered three pieces of dough. Brush the surface of the final piece with butter, too.
Scoop (or pipe) about 1 tablespoon of filling in a line on top of the dough on the side closest to you. Fold the outside pieces of dough inward, and then roll up the dough around the filling to make a cigar shape (a lot like rolling a burrito).
Transfer the cigar to the prepared baking sheet, and then repeat with the remaining dough and filling. Brush any of the remaining melted butter over the assembled cigars and sprinkle smoked paprika over each one.
Bake the cigars until golden and crisp, 17 to 22 minutes. Cool at least 5 minutes before serving warm.
Phyllo sheets vary in size slightly. Regardless of variation, the most important thing is that you get equal rectangles out of each set of 3 large sheets.