Preheat oven to 350°F (180°C). For crust: In a bowl, mix melted butter, brown sugar, and chopped pecans. Press into a 9-inch round cake pan. Bake 10-12 minutes, then cool completely.
In a large bowl, sift flour, baking powder, cocoa powder, and salt. In another bowl, cream sugar and eggs until thickened (4-5 minutes). Add vanilla and mix to combine.
Gradually add dry ingredients in thirds to the wet ingredients, alternating with milk, mixing on low speed. Scrape down the bowl and mix on high for 2-3 minutes to create a smooth batter.
Pour batter over the cooled crust. Bake the cake until a toothpick comes out clean (25-30 minutes). Let cool completely in the pan.
To fill, poke the cake with a wooden skewer, creating 1-inch spaced holes across the surface. In a bowl, mix strawberries, 1/4 cup granulated sugar, and 1 teaspoon lemon juice. Let sit for 10 minutes to release juice. Refrigerate cake 15 minutes, then carefully spoon the strawberry mixture into the poked holes, covering about 3/4 of them to prevent overflow.
Cover and refrigerate cake for at least 8 hours. Slice and serve chilled.