Place the yogurt in a large bowl and whisk until creamy, about 30 seconds. Add the remaining ingredients, whisking well to incorporate. Taste and season with more salt and pepper as needed.
Line a fine-mesh strainer or colander with a double layer of cheesecloth, and set it over a bowl or plate. Pour the yogurt mixture into the lined strainer. Refrigerate to strain for 2 to 3 hours.
To serve, unmold the cervelle de canut onto a serving dish and gently remove the cheesecloth. Serve with toasted bread, baguette, or crackers.