TO MAKE COULIS:
Lay peppers on their sides on the stovetop burner grates and turn flames on high. Char peppers, turning them with tongs, until the skins are blackened on all sides, about 10 minutes.
Transfer peppers to a bowl, cover and let them stand until they are cool enough to handle, 20 minutes. Peel peppers, then pull out the stems and remove and discard the seeds and ribs.
Blend peppers, oil, vinegar, salt, and pepper in a blender until smooth. Transfer to a bowl, cover, and reserve.
TO MAKE BREAD PUDDING:
Put rack in middle position and preheat oven to 400F.
Toss fennel, 4 tablespoons oil, herbs de Provence, salt, and pepper in a large bowl until fennel is well-coated. Transfer fennel to a large shallow baking sheet with sides, and roast , stirring once or twice, until tender and deep golden, about 25 minutes. Reserve fennel and reduce oven temperature to 350F.
Bake bread cubes in 1 layer in a large shallow baking pan until golden brown , about 6 minutes.
Cook shallots and garlic in remaining 2 tablespoons oil in a medium skillet, stirring occasionally, until softened, about 3 minutes. Reserve.
Whisk together milk, heavy cream, eggs, Parmigiano-Reggiano and Gruyere in a large bowl. Stir in roasted fennel, reserved shallot mixture, parsley, and bread cubes until well mixed. Let stand about 10 minutes for bread to absorb some of egg mixture.
While bread is soaking, butter ramekins, then put a round of parchment in bottom of ramekin and butter parchment. Spoon mixture into ramekins, then place ramekins on a baking sheet and bake until lightly golden on top and firm to the touch, 30 minutes.
To serve, run a knife around outer edge of puddings , unmold and discard parchment. Sprinkle with fennel greens, and serve with coulis.
Make ahead: Bread puddings can be made 1 day ahead. To reheat, unmold on to a foil-lined baking tray, cover with foil and heat in a 350F oven for 30 minutes.