Place the butter in a medium saucepan over high heat. Use a whisk to stir occasionally. Heat until butter starts to froth. Start to whisk often while brown flecks appear. Continue to heat and whisk until the butter turns a dark golden brown (not black).
Place the brown butter and the rest of the ingredients into a blender and puree until well combined. Taste and adjust sweetness to your liking. Pour the mixture into 12 Popsicle molds.
Place in the freezer for at least 2 hours before serving. Store covered in the freezer for up to 1 month.