Melt butter in medium saucepan over medium-low heat. Cook butter, swirling pan occasionally, for about 5 minutes or until it begins to brown.
Whisk in buttermilk, sugar, corn syrup and salt; bring to a boil. Reduce heat and simmer for 8 to 9 minutes, stirring occasionally, or until mixture is a golden brown.
Whisk in vanilla and baking soda (it will foam up). Remove from heat and keep warm while making pancakes.
In medium bowl, whisk flour, flax, baking powder, cinnamon and salt; set aside.
Spread carrots over a paper towel. Top with a second towel and gently press together.
Microwave carrots on HIGH for 2 minutes to remove moisture and soften.
In another bowl, combine carrots, buttermilk, egg, butter, brown sugar and vanilla.
Add wet ingredients to dry; mix just until dry ingredients are moistened. Do not overmix.
Spoon batter (about a heaping tablespoonful for silver dollar style pancakes) onto a lightly greased non-stick skillet or griddle over medium-low heat.
Cook about 2-3 minutes per side or until golden brown.