Combine the soy milk, honey, and vanilla in a large saucepan and heat for about 5 minutes, stirring frequently to dissolve the sugar into the soy milk. Remove from the heat, add the yogurt and raspberries, and transfer the mixture to a blender and, in batches if necessary, blend until smooth.

Turn on your ice cream maker and slowly pour the smooth soy milk and raspberry mixture into the machine; churn until it has the consistency of soft-serve ice cream, about 45 minutes. Immediately pour into a large sealable container, press plastic wrap onto the surface of the ice cream, seal the container, and freeze for at least several hours.

Remove from the freezer and let stand for 10 minutes before scooping.