Preheat oven to 350°F. Grease and flour a 9-by-13- inch baking pan; set aside.
Make streusel: Toast almonds until golden, 6 to 8 minutes, stirring halfway through. Let cool. Combine almonds with remaining streusel ingredients; mix until crumbly.
Make cake: Pat apricots dry and set aside. In a bowl, combine flour, baking powder, baking soda and salt.
In another bowl, cream butter and sugar. Beat in eggs one at a time. Mix in vanilla. Beat in half of flour mixture, mix in sour cream and stir in remaining flour mixture, scraping bowl.
Spread batter in pan. Top with a single layer of apricots. Sprinkle with streusel. Bake until a toothpick inserted in center comes out clean, 35 to 40 minutes. Cool on a rack.