1. Make the mussels: Bring water, wine, and garlic to a simmer in a large skillet. Add mussels, and cover tightly. Cook, about 2 minutes. With a slotted spoon, transfer mussels to a bowl as they open. Discard any unopened mussels. Refrigerate until chilled, at least 30 minutes.

2. Meanwhile, make the saffron mayonnaise: Simmer garlic in a small saucepan of water until tender, 15 minutes. Drain, and let cool. Crush saffron threads and 3/4 teaspoon salt with a mortar and pestle or with the back of a spoon. Puree garlic, yolks, and saffron salt in a food processor, or in a bowl using an immersion blender. With machine running, add vegetable oil in a slow, steady trickle, until mixture begins to emulsify. Continue adding remaining vegetable oil slowly, processing until incorporated. Gradually add olive oil, vinegar, and water, blending until silky. Transfer to a small bowl. (Mayonnaise can be refrigerated for up to 1 day.) Stir before serving.

3. Remove mussels from their shells, and return each one to a half shell. Spoon mayonnaise on top of each mussel, and serve with vegetables on the side and remaining mayonnaise for dipping.