Before starting, if using wooden skewers, make sure to soak them in water for at least 30 minutes to avoid burning.
Quickly prepare the Caesar dressing. Add all the ingredients to a blender and pulse until smooth. Taste and adjust seasonings, if necessary.
Reserve half of the dressing for serving and place the other half (about 1 cup) in a large bowl.
Add the tofu pieces to the bowl and toss gently to coat. Let marinate for at least 30 minutes (preferably 2 to 3 hours).
Next, trim the ends of the brussels sprouts, remove any outer brown leaves.
Bring 4 quarts of salted water to a rolling boil.
Add the brussels sprouts to the boiling water and boil until they turn bright green and just slightly tender, but still crisp, 3 to 4 minutes.
Transfer them immediately to an ice bath, cut them in half lengthwise, and pat dry.
Whisk together the olive oil, smoked paprika, and salt in a large bowl. Add the brussels sprouts and onion, tossing to coat.
When ready to grill, preheat your grill to medium-high heat for at least 10 minutes.
Thread the marinated tofu, brussels sprouts and onions onto the skewers, alternating between the 3.
Grill until the tofu is golden and slightly charred at the edges, 10 to 15 minutes, flipping and brushing with any of the leftover marinade.
Remove the skewers from the grill. Garnish with Caesar dressing, garlicky breadcrumbs and parmesan. Serve with lemon wedges and enjoy!