Preheat the oven to 350 degrees F. Butter an 8-inch-square baking pan. Line with parchment paper, leaving a 2-inch overhang on all sides. Lightly butter the paper.
Prepare the streusel: Pulse the butter, sugar, peanuts, orange zest and vanilla in a food processor just until the nuts are coarsely chopped.
Make the cake: Sift the flour, baking powder, baking soda and salt through a fine sieve into a large bowl. Beat the butter and sugar in a separate bowl with a mixer on medium-high speed until pale, about 5 minutes. Add the eggs, scrape down the sides of the bowl and beat on medium speed until fluffy, about 4 minutes. Reduce the speed to low. Add the flour mixture in 3 batches, alternating with the sour cream, beginning and ending with the flour mixture. Scrape down the bowl and finish mixing by hand (do not overmix).
Pour half of the batter into the prepared pan and smooth the top. Sprinkle with half of the streusel and dollop with half of the jam. Spread the remaining batter on top. Sprinkle with the remaining streusel and top with the remaining jam. Bake until a toothpick inserted into the center of the cake comes out clean, 50 minutes to 1 hour. Transfer the pan to a rack and let the cake cool completely, then lift out the cake by the parchment paper and cut into squares.