Meanwhile, heat 1 Tbsp. oil in a large cast-iron skillet set on grill alongside steaks. Add mushrooms and shallots to skillet and stir until mushrooms are tender and browned in spots and shallots are tender, 4–5 minutes. Remove skillet from heat; stir in brandy (caution: Mixture may ignite). Return skillet to grill. Add broth, Dijon mustard, and thyme leaves; stir to blend.