Make the stems: In a bowl, combine flour with walnut meal and baking powder. In the bowl of your electric mixer, beat the egg with the butter and sugar. Once creamy, add the flour mixture gradually until it’s all incorporated. Form the dough into a ball, wrap it in plastic wrap and chill it in the refrigerator as you prepare the other dough. Make the caps: Cream butter with sugar. When it's fluffy and pale, whisk in egg and egg yolk. Gradually add flour and baking powder and beat until you get a smooth batter. If it's too sticky add more flour. If it's too dry add a tablespoon of milk. Wrap the dough in plastic wrap and cool it in the refrigerator for at least 30 minutes. Preheat the oven to 350°F (175°C). Line a large cookie sheet with parchment paper. Take the walnut dough (for the stems) out of the refrigerator and tear it into chunks. Roll out each chunk into a thin log and cut it into 1-inch (2.5 cm) long bits.
Place the stems on your baking sheet, about 1 inch apart. Bake for about 10-15 minutes, until they rise a bit and are golden brown around the edges. Allow to cool on the baking sheet.
When the dough for the caps has been properly chilled take it out. Make 40 small balls from the dough and place them on another baking sheet, lined with parchment paper. Bake for about 10-15 minutes, until they rise and get slightly golden brown.
Once the caps are baked, start scraping out the centers immediately while they’re still hot (once cold, you won’t be able to do this). Take a small knife and make small holes in the bottom of each round cookie. Scrape out the inside, making sure you don't pierce the cookie. Store all the crumbs for later and set the hollowed-out cookies aside.
To make the filling, combine the cookie crumbs, walnut meal, cocoa, rum and jam in a bowl. Mix into a paste. Taste to see if you want to add more jam or cocoa. You need a thick, sticky filling.
Fill each mushroom cap with a bit of filling (the amount depends on the size of the hole). Then gently stick a stem into the center. Wipe away any excess filling. Set the cookies aside.
To make the chocolate glaze, place the chocolate and butter in a heatproof bowl and place it over a saucepan of simmering water. Stir occasionally until the chocolate and butter melt and the chocolate is smooth and glossy. Remove the saucepan from the heat. Dip the cookies in upside down one by one and lay them on a baking sheet.
Once all the cookies have been dipped, place the baking sheet in the refrigerator for 20 minutes or more until the chocolate has hardened. Do the same with any leftover stems.