Line an 8x8-inch pan with parchment paper, leaving overhang on two sides. In a bowl, mix almond flour, protein powder, cinnamon, and salt. Add maple syrup and melted coconut oil, stirring until mixture resembles wet sand. Press firmly into pan bottom.
Beat softened cream cheese with a hand mixer for 1 minute until completely smooth. Add Greek yogurt and beat until creamy with no lumps remaining.
Add protein powder, honey, and vanilla to cream cheese mixture. Beat on low speed first, then increase to medium until fully combined. Add 1-2 tablespoons milk if batter seems too thick.
Add eggs one at a time, beating after each just until combined. Mix in cinnamon, ginger, and nutmeg. Fold in shredded carrots with a spatula until evenly distributed throughout filling.
Pour filling over crust and smooth top with spatula. Tap pan gently on counter to release air bubbles. Cover with plastic wrap and refrigerate at least 4 hours or overnight until completely firm.
Lift bars from pan using parchment overhang. Place on cutting board and slice into 9 equal squares with a sharp knife, wiping blade clean between cuts for neat edges.