In a medium saucepan, heat oil over medium-high. Add 3/4 cup shallots; cook, stirring frequently and being careful not to burn, until golden, 3 to 4 minutes. Using a slotted spoon, transfer shallots to a paper-towel-lined plate to drain. Discard all but 1 tablespoon of the pan oil.
In same pan over medium heat, add mushrooms, carrots, ginger, jalapeno, and remaining cup shallots; season with salt and pepper. Cook until carrots have softened and mushrooms have begun to release their liquid, 3 to 5 minutes.
Add coconut milk, beef, and 3 cups water; bring to a boil. Reduce to a simmer, and cook 5 minutes. Stir in lime zest and juice; remove from heat.
Ladle soup into serving bowls; garnish with shallots and, if desired, cilantro leaves.