Place all ingredients in your food processor. Process until smooth, stopping a few times to scrape out the sides and bottom of the food processor bowl. A few specks of raspberries will remain – that’s fine.
Using a spatula, transfer the mixture into a square 8-inch pan. Cover with cling wrap, and freeze for 45 minutes.
Remove the pan from the freezer. Use a spatula to stir the already-frozen edges into the still-soft center, then use a hand whisk to mix everything together until smooth.
Cover again, and place in the freezer for 2 more hours, repeating the process of stirring the yogurt every 30 minutes.
When the entire mixture is frozen, serve immediately as a soft-serve yogurt (use chilled bowls), or freeze 1-2 more hours for a firmer consistency that you can scoop out with an ice cream scoop.
If you end up storing the frozen yogurt for longer than a few hours, remove it from the freezer 20 minutes before serving, to allow it to soften.