Place the raspberries, quartered beet, pomegranate molasses, and orange zest in a food processor or high-powered blender. Blend on high until a smooth slurry forms. Scrape down the sides with a spatula and add the chèvre and pinch of salt. Continue to blend until all the ingredients are well incorporated.
Transfer to a bowl and chill for at least an hour to encourage it to thicken. This dip keeps well covered in the refrigerator for up to 5 days.