Position rack in the center of the oven; preheat to 375 degrees F. Line a large baking sheet with parchment paper or a silicone baking mat.

Whisk all-purpose flour, whole-wheat flour, baking soda and salt in a medium bowl until well combined. Grind walnuts in a food processor until they resemble coarse meal.

Beat butter, oil, granulated sugar and brown sugar in a large bowl with an electric mixer until almost creamy--the mixture may still be a little grainy. Beat in egg and vanilla; scrape down the sides and beat in melted chocolate and the ground nuts. Stir in the dry ingredients with a wooden spoon until just incorporated.

Roll 1 tablespoon dough into a ball, place on the prepared baking sheet and flatten slightly until it looks like a deflated basketball. Continue with the remaining dough, spacing the cookies 2 inches apart.

Bake the cookies for 6 minutes. Remove from the oven and gently press your thumb or the end of a wooden spoon in the center of each cookie. Place 1/2 teaspoon jam in each indentation. Bake until the jam is melted and the cookie is set but still a little soft, 8 to 10 minutes more. Cool on the pan for 2 minutes, then transfer to a wire rack to cool completely. Let the pan cool for a few minutes before baking another batch. Enhancements: Use any flavor jam you want, just don't use preserves (the pieces of fruit may be too large) or jelly (it will melt too quickly and run).

To toast chopped walnuts: Heat a small dry skillet over medium-low heat. Add nuts and cook, stirring, until lightly browned and fragrant, 2 to 3 minutes.

Cooking Tip: To melt chocolate:

1. Bring 1 inch of water to a simmer in a double boiler set over medium-high heat, then place chocolate in the top pan. (Alternatively, to improvise a double boiler, place chocolate in a heat-safe mixing bowl that fits snugly over a pan with 1 inch of simmering water.) Stir until half the chocolate has melted. Remove the bowl and continue stirring until the chocolate has fully melted. Cool for 5 minutes at room temperature.

2. Place the chocolate in a microwave-safe bowl and microwave on High for 1 minute. Stir well, then continue microwaving in 30-second increments on High until two-thirds of the chocolate has melted, stirring well after each heating. Remove the bowl and continue stirring until all the chocolate has melted. Cool for 5 minutes at room temperature.