Preheat the oven to 425 degrees. In a small bowl, whisk the mayonnaise with 2 tablespoons of the olive oil and the garlic, lemon zest, and lemon juice; season with salt and pepper.

In a large ovenproof skillet, heat the remaining 2 tablespoons of olive oil. Add the pancetta and cook over moderate heat until golden and some of the fat has been rendered, about 4 minutes. Add the brussels sprouts, cut sides down, and the large thyme sprigs. Cook over moderately high heat, without stirring, until the brussels sprouts start to brown, about 4 minutes. Transfer the skillet to the bottom third of the oven and roast for about 10 minutes, until the brussels sprouts are tender and browned all over; discard the thyme sprigs.

Meanwhile, in another large ovenproof skillet, heat the vegetable oil until shimmering. Make 3 shallow slashes in the skin of each bass fillet to prevent curling. Season the bass with salt and pepper and add to the skillet, skin side down. Cook over moderately high heat until the skin is browned and crisp, about 4 minutes. Turn the fillets, transfer the skillet to the upper third of the oven and roast for about 4 minutes, until the fish is just white throughout.

Transfer the bass to plates, season lightly with paprika and garnish with the small thyme springs. Spoon the brussels sprouts alongside and serve right away with the garlic aioli.

The garlic aioli can be refrigerated overnight.