Prepare the mustard mayo by combining all the ingredients and stirring until well combined and smooth. Set aside.
Place the shallots and garlic in a small bowl and add red wine vinegar. Stir to moisten then set aside.
Cut baguette in half lengthwise and brush the cut side with olive oil. Grill over medium-high heat until golden and lightly charred. Season with salt and pepper. Set aside.
Place cast-iron skillet on BBQ grill or on stove-top over medium-high heat. Add 2 Tbsp. olive oil, then add tomatoes and cook, shaking the pan often to rotate the tomatoes, until they are blistered and lightly charred, about 4-5 minutes. Add tomatoes to a large bowl, then pour reserved shallot/vinegar mixture over-top. Stir to combine, then set aside to cool a bit.
If making a standard sandwich, spread mayo on one piece of the grilled bread. On the other piece of bread, place cut or torn fresh mozzarella. Sprinkle with salt, pepper and a pinch of crushed red pepper flakes. Add torn basil to slightly cooled tomatoes, season with salt, pepper and a pinch of crushed red pepper flakes and stir gently to combine. Using a slotted spoon (to leave the liquid in the bowl behind), spoon tomatoes with shallots over mozzarella. Top with other piece of grilled bread, then cut in to smaller serving pieces.
For open-faced sandwiches, prepare as above, but spread mayo on both pieces of bread and top each with mozzarella and tomatoes.