Using an electric mixer, beat the butter and sugar together until light and fluffy—5 minutes. Then add the salt, vanilla extract, and eggs with the extra yolk. Beat to combine. With the mixer running, slowly add the flour until the dough is smooth. Then separate the dough and wrap it in 4 separate pieces. Place in the fridge and chill for at least one hour. (This dough could be made weeks in advance.)
When ready to bake, preheat the oven to 375 degrees F. Line several cookie sheets with parchment paper. Remove one disk from the refrigerator at a time to keep the dough cold as long as possible. Flour a work surface and roll the disk out to 1/8-inch thick. Using 1- to 2-inch heart cookie cutters, cut out the cookies. (You can use multiple sizes if desired.) Work fast and cut the cookies as close together as possible. The more times you roll out the dough, the tougher it gets. Then use a straw to cut out a hole close to the bottom point of each heart. With a thin spatula, transfer the cookies onto the baking sheets 1 inch apart. Repeat with remaining dough. For the toppers: Insert lollipop sticks into 3-5 of the largest cookies. Press down a little to insure the cookies adhere to the sticks while baking. (I like to make extras just in case one breaks.) Bake the cut out cookies for 6-9 minutes, until just cooked through. Cool completely on the cookie sheets before moving.
For the Strawberry Glaze: Whisk the milk, strawberry extract, and powdered sugar together until smooth. Dip and face of each cookie into the glaze. Allow the excess to drip off the tip, then scatter sprinkles over the top. Place the cut out cookies back on the parchment paper to dry.
Once all the cookies are dipped, sprinkled and dried, start building your heart tree(s). Pin the largest hearts at the base of the cone with the point up. Push the pin (or toothpick) through the hole you cut in each cookie, and press firmly into the styrofoam cone. It's best if the edges of each cookie overlap just a little. Then start the next row with the center of each heart lined up with the overlap. Continue moving up the cone, using the smallest cut out cookies at the top. Before you cover the top of the cone, press one of the heart cookie pops down in the center as a decorative topper. Then finish covering the top of the styrofoam. Repeat with the remaining cookies and cones. If you roll your dough thin, then cut the cookies out very closely together, you should have enough for three 12-inch heart trees. **If you plan to allow children to remove cookies from the heart tree later, it's best to use toothpicks instead of pins.