Position rack in middle of oven. Preheat oven to 350° F.
Coat an 8-inch square pan with nonstick spray.
Whisk together flour, baking soda and salt in a medium bowl to aerate and combine; set aside.
Beat butter with flat paddle on medium-high speed until creamy, about 1 minute. Add sugar and beat until light and fluffy, about 3 minutes, scraping down the bowl once or twice.
Beat in egg until well combined. Add the flour mixture in two additions, alternately with the buttermilk. Begin and end with the flour mixture and beat briefly until smooth.
Scrape batter evenly into pan and smooth top with offset spatula. It will be a fairly shallow layer. Scatter blackberries evenly on top, reserving about 5 of them; do not press into batter. They will sink during baking. Bake for about 15 to 25 minutes or until a toothpick shows a few moist crumbs. The cake will just have begun to come away from the sides of the pan. Cool pan completely on rack.

Combine brown sugar, butter and cream in small saucepan and bring to a simmer over medium-high heat. Simmer for 1 minute, whisking frequently.
Remove from heat and whisk in vanilla and confectioners' sugar until smooth and fluid. It will firm up very quickly and if you whisk or cool it too long, it will become too firm and sugary.
Drizzle half of the icing with a spoon all over top of cake, then quickly sprinkle walnuts and reserved berries evenly over top while icing is still wet. Drizzle with remaining icing, which will set up almost immediately. Store at room temperature well wrapped in plastic wrap up to 1 day.

You might be tempted to add extra berries to the batter, but they add too much moisture and will throw off the balance of the cake. The amount called for along with the shallow cake layer, are well proportioned as is. Also, when making the icing, make sure you stop combining the ingredients the moment the mixture becomes smooth. If it becomes grainy and sandy you have stirred too long and must start again.