In a large bowl, beat softened cream cheese and butter together with an electric mixer on medium speed until completely smooth and creamy (about 2-3 minutes). No lumps should remain. Add pumpkin puree, vanilla extract, and salt, and beat on medium-low speed until well combined. Scrape down the sides of the bowl.

With mixer on low speed, gradually add powdered sugar, ½ cup at a time, beating well after each addition. The mixture will start thick and crumbly, then become smooth and spreadable. Add pumpkin pie spice, cinnamon, nutmeg, ginger, and cloves. If using maple syrup, add it now. Continue beating until mixture is very thick and holds its shape when you lift the beaters (about 3-4 minutes total).

Line an 8x8 or 9x9 square baking pan with parchment paper, leaving an overhang on two sides for easy removal. If using nuts or chocolate chips, fold them into the fudge mixture now with a spatula. Transfer mixture to prepared pan and press down firmly and evenly with the back of a spoon or your hands (lightly greased). Smooth the top.

Cover with plastic wrap and refrigerate for at least 3 hours, or until completely firm. Once firm, lift fudge out of pan using parchment paper overhang. Place on cutting board and use a sharp knife to cut into 1-inch squares. Wipe knife with damp cloth between each cut for clean slices. Store in airtight container in refrigerator for up to 2 weeks.