Melt the butter in a medium saucepan over medium heat.
Add the onion and cook until softened, about 2 minutes.
Add the garlic and cook until the onion is translucent, about 2 minutes.
Sprinkle in the flour, stir well, and cook without browning for 1 minute.
Whisk in the oil, vinegar, lemon juice, mustard and sugar.
Bring to a boil and reduce the heat to medium low.
Add the parsley and cook, whisking often, until lightly thickened, about 5 minutes.
Let cool -- the baste will separate -- whisk well before using.