Preheat the oven to 350 F. Butter a 9-inch square baking pan or dish.
In a large bowl or food processor, combine the flours, brown sugar, salt, baking powder, and baking soda. Pulse or stir to combine. Scatter the butter pieces over the flour mixture and cut in the butter with a pastry cutter or two kitchen knives until the mixture is moist and crumbly (or pulse in food processor until it looks like coarse sand). Add the oats and nuts, if using, and stir to mix evenly (don't use food processor here - just a spoon).
Press two-thirds of the dough into the bottom of the prepared pan. Spread the jam as evenly as you can over the top - using 1/2 cup if less sweetness is desired, 1 cup for more (I use closer to 1 cup... whatever it takes for the jam to be all over in a thin layer. It will look messy, but don't worry - the jam will spread as it bakes). Crumble the remaining oatmeal mixture evenly over the top, and press down lightly.
Bake until the top is golden brown, 35-40 minutes. Let cool completely on a rack, and then cut into bars.
Source: slightly adapted from Williams-Sonoma's Family Meals Cookbook by Maria Helm Sinskey