Cut a double thickness of cheesecloth into eight 5-by-8-inch pieces. Line 8 individual coeur a la creme molds (see Note) with cheesecloth, leaving a generous amount of overhang. Line a baking sheet with sides with several layers of paper towels. Place a large wire rack on baking sheet and set prepared molds on rack. (Alternatively, cut the sides of eight 12-ounce paper cups to make shorter cups 2 to 3 inches high. With a toothpick, punch about 10 holes slightly with the toothpick. Line cups with cheesecloth and place on rack.)
Combine cream cheese, sugar, lemon zest and vanilla in a food processor and process until very smooth, scraping down sides occasionally. Add yogurt and process to blend.
Spoon mixture into the prepared molds. Cover with plastic wrap; drain in the refrigerator overnight.
To serve, invert coeurs a la creme onto dessert plates and carefully remove cheesecloth. Surround with sauce and garnish with lemon zest and mint.
Make Ahead Tip: Prepare through Step 3 up to 2 days in advance.
Equipment: 8 coeur à la crème molds or 12-ounce paper cups
Coeur a la Creme molds can be mail-ordered from www.cookswares.com.