How to Make It
In a small skillet, heat 1 tablespoon of the vegetable oil. Add half of the shallots and cook over moderately low heat, stirring frequently, until softened and golden, about 10 minutes. Add the vinegar and cook over moderately high heat until reduced by half, about 5 minutes. Transfer the contents of the skillet to a blender and let cool. Add the mustard and blend until smooth. With the machine on, add the remaining 1/4 cup plus 1 tablespoon of vegetable oil in a thin stream and blend until emulsified. Season the dressing with salt and pepper.
In a large skillet, fry the bacon over moderately high heat until crisp, about 7 minutes. Drain the bacon on paper towels. Pour off the fat from the skillet. Add 2 tablespoons of the olive oil to the pan and heat until shimmering. Add the oyster mushrooms and garlic and cook over moderate heat, stirring occasionally, until the mushrooms are tender and browned, about 8 minutes. Scrape the mushrooms into a large bowl.
Heat the remaining 2 tablespoons of olive oil in the skillet. Add the cremini mushrooms and the remaining shallots and cook over moderate heat until golden and tender, about 10 minutes. Add the mushrooms to the bowl and season with salt and pepper. Add the frisée, the cooked bacon and the vinaigrette, season with salt and pepper and toss. Transfer the salad to plates and serve right away.