Put the empty loaf pan or storage tub in the freezer while you work. A cold container starts setting the base the moment it goes in, which is where a smooth texture begins.
Whisk the cocoa powder with the honey and vanilla into a smooth, glossy paste. Cocoa is hydrophobic and clumps the instant it hits liquid, so hydrating it in the honey first is what keeps the base free of dry pockets.
Whisk the Greek yogurt and salt into the cocoa paste until it is completely smooth. This is the flavour base.
In a separate cold bowl, whip the heavy cream only to soft peaks, the point where a lifted whisk leaves a peak that flops over on itself. Stop there. Whipped to stiff peaks the cream turns the finished ice cream dense and almost buttery.
Fold a third of the whipped cream into the cocoa base to slacken it, then fold in the rest until no pale streaks remain. Fold, never stir. Stirring beats the air back out and the scoopable texture goes with it.
Fold in most of the chopped chocolate, holding back a small handful.
Scrape into the chilled container, level the top, scatter on the reserved chocolate, and press a piece of parchment or wrap directly onto the surface so ice cannot form on top.
Freeze at least 6 hours or overnight, until firm. Let it stand on the counter 5 to 10 minutes before scooping.