Add all ingredients except the oil to a blender or food processor and process until pureed. With the motor running, add the oil in a thin stream and process until emulsified. It will keep for 1 week in the refrigerator in an airtight container.
In a small mixing bowl, whisk together all ingredients expect the blue cheese until fully combined. Fold in the blue cheese, making sure to leave some pieces in larger chunks for added texture. Taste and adjust seasoning, adding more salt, sugar or acid to balance your particular cheese.
This has a nice garlic kick at the end which I love with the other flavors. If you don't like the lingering taste of raw garlic, replace it with a little minced shallot.
Place all ingredients except the lemon juice in a medium saucepan and mix to combine. Bring to a boil, then reduce to a simmer and cook, stirring occasionally, until most of the liquid has evaporated but with a small amount of syrupy liquid remaining. Transfer to a small, air-tight jar and cool to room temperature. Taste, adding lemon juice as needed to balance the sweetness. Store in the refrigerator for up to 2 weeks.