Heat a large cast-iron skillet over medium-high to high. Bring the steaks to room temperature. Pat dry and season on both sides with kosher salt and black pepper.
Prepare a large bowl of ice water. In a large saucepan, bring a couple of inches of water to a boil. Salt the water, add the haricots verts and cook until crisp-tender, about 2 minutes; drain. Place the haricots verts in the ice water and let cool. Drain and pat dry.
Add the oil, one turn of the pan, to the hot skillet. Add the steaks and half the rosemary. Cook the steaks 8 minutes, turning occasionally; transfer to a plate and let rest.
Add 2 tbsp. butter to the skillet. When the butter melts, add the mushrooms and the remaining rosemary. Cook, stirring often, until the mushrooms brown, about 8 minutes. Add the shallots and haricots verts; season and cook, stirring often, until the shallots soften, 2 to 3 minutes. Mix in the stock; transfer to a serving dish.
Add the garlic and the remaining 2 tbsp. butter to the skillet. Cook, stirring often, until fragrant, about 1 minute. Add the wine and cook, stirring occasionally, until the sauce is reduced by half, 5 to 7 minutes. Add the lemon juice and remove the skillet from the heat.
Slice the steaks against the grain. Arrange on plates and top with the white wine sauce. Serve the haricot verts and mushrooms alongside.