Combine the peanut butter with the liquid Erythritol in a small saucepan, stirring over low heat. Add the vanilla extract and mix well.
In a large mixing bowl, combine the almond flour, cinnamon, salt, and granulated Erythritol and mix to combine. Fold in the grated carrot.
Add the peanut butter mixture and butter and stir well.
Gradually add the milk in a stream while mixing until you get a thick yet fudgy consistency.
Line an 8x8-inch container with baking paper and spread the dough in. Level with the back of a spoon and place in the fridge while you are making the frosting.
In the meantime, make the frosting: In a large mixing bowl, whisk together the cream cheese with the cinnamon and powdered Erythritol.
Spread over the carrot bars and refrigerate until firm, or serve straight away for a softer texture.