Preheat your oven to 375°F and lightly grease a 9x13-inch baking dish. Bring a large pot of salted water to a boil, add the green beans, and cook for 5 minutes until bright green and crisp-tender, then drain and transfer to the prepared baking dish.
Melt the butter in a large skillet over medium heat. Add the diced onion and minced jalapeños, cooking for 4-5 minutes until softened. Stir in the minced garlic and cook for 30 seconds until fragrant.
Add the sliced mushrooms to the skillet and cook for 6-7 minutes, stirring occasionally, until they have released their liquid and turned golden brown.
Sprinkle the flour over the mushroom mixture and cook for 1 minute while stirring constantly to form a paste. Gradually whisk in the milk, broth, and heavy cream until the mixture is smooth and begins to thicken, about 3-4 minutes.
Stir in the salt, black pepper, and smoked paprika, then remove the skillet from heat. Pour the creamy mushroom mixture over the green beans in the baking dish and stir gently to combine everything evenly.
Sprinkle the shredded pepper jack cheese evenly over the top, followed by the french fried onions. Bake uncovered for 25-30 minutes until the casserole is bubbling vigorously around the edges and the topping is golden brown.