To Make the Mushy Peas:
Heat butter in a small saucepan over medium. Cook onion, stirring occasionally, until softened but not browned, about 5 minutes. Add peas and stock and season with salt and pepper. Bring to a boil; reduce heat and simmer until peas are bright green and tender, about 5 minutes.
Transfer to a food processor, add mint, and pulse to a coarse puree; season with salt and pepper.
Peas can be cooked 1 day ahead. Let cool; cover and chill.
To Assemble Fish And Chips:
Fit a large pot with thermometer; pour in oil to measure 4". Heat over medium-high until thermometer registers 250°. Add half of potatoes and fry, stirring occasionally, until potatoes are tender and cooked through but have not taken on any colour, 10–12 minutes. Using a spider or slotted spoon, transfer to paper towels to drain. Repeat with remaining potatoes.
Increase heat to bring oil to 325°. Whisk beer, soy sauce, cayenne, and 1½ cups flour in a large bowl until no lumps remain; season with salt and pepper. Place remaining ½ cup flour in a shallow bowl. Season haddock with salt and pepper and dredge lightly in flour.
Working with 2 pieces at a time, dip fish into batter, letting excess drip back into bowl. Carefully lower fish into oil and fry until fish is cooked through and batter is golden brown and crisp, 8–10 minutes. Transfer fish to paper towels to drain; season with salt.
As soon as all fish is fried, add potatoes to oil and fry until crisp and golden, about 4 minutes. Using a spider or slotted spoon, transfer chips to paper towels to drain; season with salt.
Meanwhile, gently reheat mushy peas over medium heat, if needed. Serve alongside fish and chips.