Bring a large pot of water to a rapid boil. Add green beans, then cook. Immediately transfer to an ice bath to cool. While they cool, cook the almonds.
Melt unsalted butter in a skillet over medium heat. Add sliced almonds, then toast, shaking the pan occasionally, until golden brown and fragrant. Using a slotted spoon, transfer the almonds to a small bowl.
To the same pan, add olive oil and warm over medium heat. Add chopped shallot, season with kosher salt, then cook, stirring occasionally, until softened. Add chopped garlic, then cook.
Drain the green beans. Increase the heat to medium-high, then add the green beans to the skillet. Season with remaining kosher salt and black pepper, then cook, stirring occasionally, until tender.
Transfer to a serving plate, then sprinkle the toasted almonds on top. Finish with a pinch of flaky sea salt. Enjoy!