In a large pot, bring salted water to a rolling boil. Add the trimmed green beans and blanch for about 3-4 minutes until they are bright green and tender-crisp. Drain the beans in a strainer and immediately plunge them into a bowl of ice water to stop the cooking process.
In a medium skillet over medium heat, melt the unsalted butter. Add the minced garlic and sauté for about 1 minute until fragrant. Remove from heat and mix in the panko bread crumbs, cheddar cheese, jalapeno pepper cheese, and half of the kosher salt. Stir until well combined.
In a large mixing bowl, toss the blanched green beans with olive oil, remaining kosher salt, and ground black pepper. Make sure the beans are evenly coated.
Transfer the green beans to the prepared baking sheet. Evenly distribute the cheesy breadcrumb mixture over the top of the green beans, making sure to cover them well.
Preheat your oven to 400°F (200°C). Once preheated, place the baking sheet in the oven and bake for about 15-20 minutes, or until the cheese is melted and the breadcrumb topping is golden brown and crispy.
Once out of the oven, let the green beans cool for a minute before serving. They are best enjoyed warm and fresh.