Bring 4 quarts water to a rolling boil in a large pot, then stir in 2 tablespoons kosher salt.
Trim the green beans and boil until crisp-tender, 4β5 minutes (3β4 minutes for thin haricots verts). Drain very well.
While the water heats and the beans cook, toast the sliced almonds in a large dry skillet over medium heat, stirring, until golden and fragrant, 3β4 minutes. Transfer to a bowl.
Return the skillet to medium heat. Add the unsalted butter and olive oil; when the butter is foamy, add the minced shallot and cook, stirring, until translucent and softened, 1β2 minutes.
Add the drained green beans to the skillet and toss to coat in the butter mixture. Cook, stirring, until glossy and heated through, 2β3 minutes.
Off the heat, add the lemon juice, lemon zest, parsley, and black pepper. Return the toasted almonds to the pan and toss until evenly distributed.