Into a large Dutch oven fitted with a deep-fry thermometer, pour 10 cups oil (about a depth of 3"). Heat over high heat until thermometer registers 375°.

Meanwhile, pat steak dry; season all over with salt. Heat a large stainless steel skillet over medium-high heat. When pan is very hot, pour in 1 tablespoon oil and swirl to coat pan. Cook steak, turning halfway through, until a brown crust forms and an instant-read thermometer inserted into thickest part registers 125°, 2 to 3 minutes per side. Transfer steak to a cutting board.

In same skillet over medium heat, cook olives, stirring occasionally, until starting to brown, about 2 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute. Add gin and vermouth and stir to deglaze pan. Bring to a simmer and cook, stirring occasionally, until liquid is almost evaporated, 4 to 5 minutes. Add broth and simmer, stirring occasionally, until reduced by about two-thirds, about 5 minutes. Remove from heat and stir in olive brine and butter.

While sauce simmers, using a spider, add half of fries to hot oil and agitate to break up any clumps. Fry until crispy and cooked through, 3 to 4 minutes. Transfer to a paper towel-lined baking sheet; season with salt. Repeat with remaining fries.

In a large bowl, whisk mustard, vinegar, honey, and a pinch of salt. While whisking, drizzle in remaining 4 tablespoons oil until dressing is smooth and combined. Add mixed greens and parsley and toss in dressing until coated.

Slice steak against the grain. Transfer to a platter. Top with olive sauce and blue cheese (if using). Serve with fries and salad alongside.