Preheat oven to 350 degrees F. Spray a 9-inch cake pan with cooking spray, and flour the pan well. Discard any loose flour, and set aside.
In a small saucepan, melt butter over medium-low heat, and cook until the butter has started to turn golden brown, approximately 7-8 minutes. Be careful not to let it turn too dark or burn. Remove from heat and let cool for 5 min.
With a stand mixer and paddle attachment, beat the brown butter and sugar together until creamy on medium speed, about 3 minutes. Scrape the sides down, and add egg. Continue to beat on medium speed for a couple minutes, incorporating egg thoroughly.
In a medium bowl, whisk together flour, baking soda and salt. Turn mixer to low speed, and alternate between adding flour mixture and buttermilk a little at a time each, starting and ending with flour mixture. Beat together only until the mixtures combine, careful not to overmix the batter.
Combine the blueberries, lemon zest and lemon juice in a small bowl, and toss together. Fold in half of the blueberries to the batter gently with a spatula or wooden spoon, and pour the mixture into cake pan. Add the other half of blueberries as an even layer on top of batter. Sprinkle crumble evenly over blueberries.
Bake for 40 minutes, or until crumble turns golden color. Remove from oven, and cool on rack. Serve warm, or let cool completely and store in refrigerator under sealed plastic wrap.
In a medium bowl, whisk together flour, sugar, brown sugar, salt and cinnamon. Stir in melted butter with a fork until crumbs begin to form. Stir in chopped walnuts and combine thoroughly.