Heat the oven to 350 degrees. Butter a 9-inch square baking pan. Line the pan with parchment paper, leaving a 2-inch overhang on two sides.
Prepare the bars: In a large bowl, lightly beat the eggs. Add the maple syrup and melted butter and whisk to combine. Add the flour, oats, vanilla, cinnamon, salt and baking soda and whisk until well-combined. Spread the batter evenly in the prepared pan.
Dollop the apple butter evenly on top of the batter. Swirl it around just to make sure it’s evenly distributed. (Don’t worry about decorative swirls.)
Make the topping: In the same bowl, stir together the flour, oats, butter, brown sugar, cinnamon and salt. Squeeze the mixture into clumps and sprinkle evenly over the top of the batter.
Bake until a toothpick inserted into the center (avoiding pockets of apple butter) comes out with moist crumbs attached, about 30 minutes. Transfer to a rack to cool.
To serve, use the parchment paper overhang to lift the bar out of the pan and transfer to a cutting board. Cut into 9 or 12 even pieces. Store in an airtight container at room temperature for up to 3 days. (You could also freeze for up to 3 months; thaw at room temperature before serving.)
