Preheat your oven to 325°F (163°C). In a mixing bowl, combine crushed graham crackers, sugar, and melted butter until the mixture resembles wet sand. Line an 8x8 inch baking pan with parchment paper for easy removal. Press the crumb mixture firmly into the bottom of the pan, ensuring it's even and slightly pressed up the sides for added structure.

In a large mixing bowl, beat the room-temperature cream cheese and sugar using an electric mixer until smooth and creamy, about 2-3 minutes. Add eggs one at a time, mixing well after each addition, then blend in the vanilla extract. Gently fold in the ricotta cheese and mini chocolate chips until just combined, ensuring not to overmix.

Pour the creamy filling over the prepared crust, spreading it evenly with a spatula. Bake in the preheated oven for 40-45 minutes, or until the edges are set and the center jiggles slightly when gently shaken.

Once baked, remove the pan from the oven and allow it to cool at room temperature for about 1 hour. After an hour, cover the bars and refrigerate for at least 4 hours, preferably overnight, to ensure they firm up beautifully.

When ready to serve, dust the chilled Cannoli Cheesecake Bars with powdered sugar for an elegant touch. Cut into squares or rectangles and enjoy.