Preheat oven to 375 degrees. Line a baking sheet with parchment paper. Place one sheet of phyllo dough on a clean, dry work surface; cover remaining sheets with a damp kitchen towel. Using a pastry brush, brush phyllo lightly with melted butter. Place 2 teaspoons confectioners' sugar in a fine sieve; dust phyllo with sugar. Top with a second sheet of phyllo dough. Brush with melted butter; dust with sugar. Continue this process with the remaining 5 sheets of phyllo dough.
Fold the stack in half, forming a 7-by-6 1/2-inch rectangle; transfer to baking sheet. Chill until the butter solidifies, about 10 minutes.
Using a coeur a la creme mold as a guide, cut out four hearts from the layered phyllo dough with a paring knife; remove excess dough from the baking sheet, and discard.
Bake phyllo hearts until golden brown, about 10 minutes. Transfer to a wire rack until cool. Store in an airtight container.
Cut out four 6-inch squares of cheesecloth. Dampen squares with water, line the coeur a la creme molds, and set aside.
Place cottage cheese and 1 tablespoon sugar in the bowl of a food processor fitted with the blade attachment. Process until smooth, about 2 1/2 minutes. Add cream cheese; pulse until smooth, about 1 minute. Add yogurt, and pulse 15 seconds. Divide cheese mixture evenly among molds, about 3/4 cup per mold. Fold the overhanging cheesecloth over the tops. Place molds on an unlined baking pan, and transfer to refrigerator. Allow mixture to drain 4 hours or overnight.
If using, cut pomegranate in half, and reserve 2 tablespoons seeds for garnish. Transfer the remaining seeds to the bowl of a food processor; puree 30 seconds. Transfer puree to a fine sieve set over a medium bowl. Using the back of a ladle, push down on pulp to extract juice. Whisk remaining teaspoon sugar into juice.
When ready to serve, place the reserved phyllo hearts on plates. Lift cheesecloth from molds, and invert the cheese hearts onto the phyllo hearts; remove cheesecloth. Drizzle the juice over the assembled hearts. Garnish desserts with pomegranate seeds and rose petals, if using; serve immediately.