Lightly butter a 9 x 13 baking pan and dust all sides with flour, removing excess. Set aside.
Sift together flour, sugar, baking powder, and salt in a medium-sized bowl and set aside. In a separate medium-sized bowl, whisk egg, melted butter, cream, canola oil, sour cream, and vanilla together.
Gently fold the wet and dry ingredients together using a rubber spatula.
Spread cake mixture into your prepped baking pan.
Now, it's time for the layers!
Layer the cream cheese mixture on top of the cake batter. Add the crumbs to the top of the cream cheese layer.
Now the fun part!
Drizzle the coulis on top. To make this easy, pour the coulis into a ziploc or pastry bag, and nip off the end of the bag.
Place the pan in your pre-heated oven and bake for 14-15 minutes. Rotate pan.
Bake another 10 minutes. Use a cake tester to verify done-ness (but don't be fooled, because it's difficult to tell with the cream cheese layer)!
Be careful to not cook it to long (25 minutes seems to be just about right (at least it was in my oven)). Your oven temperature may vary.
Let cake cool before slicing.