Trim a thin slice from each side of the long axis of each potato. Once each potato is "squared," slice it into 1/4-inch planks and then cut each plank into 1/4-inch fries. Rinse cut potatoes in large bowl under cold running water until water turns clear. Cover with cold water and refrigerate for 30 minutes or up to 12 hours.
Pour off water, spread potatoes onto kitchen towels, and thoroughly dry. Transfer potatoes to large bowl and toss with cornstarch until evenly coated. Transfer potatoes to wire rack set in rimmed baking sheet and let rest until fine white coating forms, about 20 minutes.
Meanwhile, in heavy-bottomed 7 qt Dutch oven fitted with clip-on-the-pot candy thermometer, heat peanut oil over medium heat to 325 degrees F.
Add half of potatoes, a handful at a time, to hot oil and increase heat to high. Fry, stirring, until potatoes start to turn from white to blond, 4 to 5 minutes. (Oil temperature will drop about 75 degrees during this frying.)
Transfer fries to thick paper bag or paper towels. Return oil to 325 degrees F and repeat with remaining potatoes. Reduce heat to medium and let fries cool while cooking steaks, at least 10 minutes.
Combine all herb butter ingredients in medium bowl. Set aside. Heat vegetable oil in 12-inch skillet over medium-high heat until smoking.
Meanwhile, cut your steaks in half. If your steaks are 1 1/4 to 1 3/4 inches thick, cut them in half vertically into small, thick steaks. If your steaks are thicker than 1 3/4 inches, cut them in half horizontally into two thinner steaks.
Next, season steaks with salt and pepper. Lay steaks in pan, leaving 1/4 inch between them. Cook, not moving steaks, until well browned, about 4 minutes.
Using tongs, flip steaks and continue to cook until instant-read thermometer inserted in center registers 120 degrees F for rare to medium-rare, 3 to 7 minutes. Transfer steaks to large plate, top with butter, and tent loosely with foil; let rest while finishing fries.
Increase heat under Dutch oven to high and heat oil to 375 degrees. Add half of fries, a handful at a time, and fry until golden brown and puffed, 2 to 3 minutes. Transfer to a thick unopened paper bag or paper towels. Return oil to 375 degrees F and repeat with remaining fries. Season fries with salt and serve immediately with steaks.