Place milk in a 2-quart saucepan; sprinkle with gelatin and let stand 1 minute. Heat milk and gelatin and stir until smooth. Stir in sugar and espresso powder; cook until sugar is dissolved. Transfer to a medium bowl and cool.
Add yogurt and half-and-half, stir until completely blended.
Turn the machine on; pour the mixture into freezer bowl, and let mix until thickened, about 20 to 25 minutes. The frozen yogurt will have a soft, creamy texture.
If a firmer consistency is desired, transfer the frozen yogurt to an airtight container and place in freezer for about 2 hours. Remove from freezer about 15 minutes before serving.