Place a macaron mat on each of 2 baking sheets. You can also use parchment paper with 1-inch circles drawn on underneath. Set these aside.

Place a medium round tip, like a #12, in a disposable piping bag with a plastic tip coupler to keep it in place. Twist the bag just above the tip and secure with a small binder clip. Fold over the top of the bag and place it in a tall glass or in a piping bag holder so it will be easy to fill with the batter. Set this aside.

Place the egg whites in the bowl of a stand mixer fitted with the whisk attachment and beat on medium-high until frothy. Add the cream of tartar, then slowly add the granulated sugar, one spoonful at a time, with the mixer still running.

Using a silicone spatula, carefully fold ⅓ of the flour/powdered sugar mixture into the meringue. Then, add the remaining ⅔ of the flour mixture and continue folding until just before reaching the figure 8 stage. See note.

Once the batter is the proper consistency, transfer it to the prepared piping bag.

Slam the tray down hard on the counter or a table several times to force any air bubbles to the surface. If desired, take a toothpick or scribe tool and pop large bubbles then smooth out the hole left after the bubble pops.

Place the chocolate in the top of a double boiler and melt above simmering water (or use microwave to melt, being careful to heat on 50% power and for short amounts of time, stirring often). The chocolate should be just melted and only warm, not hot.

Bring the cream just to a boil in a small saucepan. As soon as it boils, remove from heat and pour the hot cream over the chocolate.

Stir very gently with a rubber spatula until the mixture is smooth and shiny.

Allow the ganache to cool at room temperature, stirring occasionally, until it is a pipable consistency.

Bake the macaron shells for 12-15 minutes, rotating the pan once about 7 minutes into the bake. Only bake one pan at at time.

Allow the shells to cool completely on the mats before removing them. To remove more easily, push up on the mat from underneath to help them pop off. If you have trouble with them sticking, that may mean they are underbaked. Some of the shells in the center of the tray may have a little bit of sticking. Very carefully use a stiff metal spatula to pry them off the mat, taking care not to rip the shell.

The cooled shells can be stored in an airtight container in the refrigerator or freezer, or you can fill them immediately.

Because the macarons will be sandwiched, pair up the shells by size. You want the top and bottom of the sandwich cookie to match as closely as possible.