Whisk the 2 egg whites, 1/2 cup sugar, 1/8 tsp salt, and 1/8 tsp cream of tartar together on high speed for about 7 minutes, continuing until the mixture holds its shape. Look for a shiny foam that leaves ribbons behind the whisk and forms fairly stiff peaks.
Fill a piping bag fitted with a 3/8-inch round tip, then pipe the caps about 1 inch apart with bases approximately 1 1/2 inches across, sweeping the tip sideways to finish each top. A rounded dome is the goal, and a wet fingertip can gently flatten any remaining point.
Pipe the stems with bases approximately 3/4 inch across, making them narrower and taller than the caps. Each stem should taper upward to a pointed tip.
Bake the pieces at 200°F for 1 hour 30 minutes, checking that they release readily from the parchment. The outside should feel crisp, although the center may still have a slightly soft, marshmallow-like texture.
Lift the parchment and cookies off the hot baking sheet and let them reach room temperature on the paper. The meringues will firm throughout as they cool completely.
Lightly dust the cooled caps and stems with cocoa, optionally rubbing it with your fingertips, then use a small paring knife to make a recess in the center of each cap's underside. Keep each opening just large enough to receive a stem tip, with only a light cocoa shading on the surface.
Melt the chocolate chips, spoon the chocolate into a zip-top bag, snip a tiny opening in one corner, and squeeze chocolate into each cap recess before inserting a stem. Rest the mushrooms upside down on their caps until the chocolate becomes firm and holds the stems in place.
Move the assembled mushrooms gently into an airtight container and keep them at room temperature rather than refrigerating them. The chocolate joints should be fully set before you handle the finished cookies.