In a large, resealable plastic bag, combine the flour and 1/4 teaspoon each salt and pepper. In an extra-large skillet, heat 3 tablespoons olive oil over medium heat. Rinse half of the mushrooms quickly and shake in the bag of seasoned flour, then add to the pan and cook, turning once or twice, until golden, 6 to 7 minutes. Transfer to a plate. Repeat with the remaining mushrooms and 3 tablespoons olive oil.
Add the scallions to the pan, lower the heat to medium-low and cook, stirring, for 1 minute. Carefully pour in the cognac, simmer until nearly evaporated, then stir in the peppercorns, bouillon base and 1 cup water. Bring to a simmer, then stir in the cream and mustard. Return the mushrooms to the pan and simmer, turning the mushrooms occasionally, until the sauce is thickened, about 3 minutes. Transfer the mushrooms to serving plates and continue to simmer the sauce until thick enough to coat the back of a spoon, about 3 minutes; season with salt and pepper. Spoon the sauce over the mushrooms.