Reduce heat to medium and pour remaining 1 Tbsp. oil into pan. Cook shallots, stirring often, until softened, about 2 minutes. Add garlic; cook, stirring, until softened, about 1 minute. Add tomato paste and cook, stirring constantly, until slightly darkened in color, about 2 minutes. Add flour and cook, stirring often to coat shallots and garlic, until toasty smelling, about 3 minutes. Add wine; cook, scraping up browned bits, until evaporated, about 1 minute. Add broth, fish sauce, and any liquid from mushrooms (leave mushrooms behind). Bring to a boil over high heat, then reduce heat; simmer, stirring occasionally, until sauce coats a spoon, 12–15 minutes.