In a large skillet, heat 2 teaspoons oil over medium-high and cook one-third the mushrooms, stirring occasionally, until golden brown, about 4 minutes. Season with salt and pepper and transfer to a large bowl. Repeat with more oil and remaining mushrooms. Add 2 teaspoons oil to skillet and cook asparagus, stirring occasionally, until crisp-tender, about 4 minutes. Season with salt and pepper and add to mushrooms. Add 1 teaspoon oil to skillet and cook shallot until translucent, 3 minutes. Add vinegar and mustard and stir to combine. Add broth and cook, scraping up any browned bits with a wooden spoon, until slightly thickened, about 1 minute. Stir in honey, then pour over vegetables. Toss to combine and transfer to a serving dish. Serve warm or at room temperature (toss before serving).