In a small bowl, sprinkle gelatin over 1/2 cup milk. Let stand 1 minute, then stir and let stand about 10 more minutes for gelatin to soften.
In a medium saucepan, whisk remaining 1 1/2 cups milk, the sugar, semisweet chocolate, and cocoa over medium-high heat until steaming, about 3 minutes. Add gelatin mixture and whisk gently until it dissolves, 2 to 3 minutes. Let cool 15 minutes.
In a large bowl, whisk yogurt with vanilla until smooth. Pour and stir chocolate mixture through a fine strainer into yogurt, then whisk mixtures together.
Oil 8 ramekins (2/3 cup size). Divide yogurt mixture among ramekins. Chill, covered, until set, 4 1/2 hours and up to 2 days.
Run a small metal spatula between panna cottas and sides of ramekins to loosen. Immerse ramekins 1 at a time to just below rim in hot water until edges of dessert soften, 20 to 30 seconds; lift out and dry bottom of ramekin. Invert a small plate over each. Hold plate and ramekin together and give a firm shake to release panna cotta, easing it out gently with the spatula if needed.
Scatter chocolate shavings over desserts if you like.
Note: Nutritional analysis is per serving.