Cut the potatoes into lengths of about ¼” x ¼” x 4”. Place the cut up potatoes into a large bowl. Fill the bowl with enough cold water to cover the potatoes and refrigerate for 2 hours.
Heat the butter in a large, deep skillet over medium heat. Once the butter has melted whisk in the flour and cook while whisking until smooth (about 2 minutes). Add the minced shallot and garlic and cook until soft (about 2 more minutes). Add the beef broth a little at a time while whisking. Whisk in ketchup, vinegar, and Worcestershire sauce. Season with salt and pepper. Bring to a boil while whisking. Cook while whisking until the mixture has thickened (about 6 minutes). Keep the gravy warm.
Heat oil in a deep-fryer to 325 degrees F. Drain the water from the potatoes and dry them with paper towels. Fry the potatoes in small batches tossing occasionally until tender and slightly crisp (about 4 minutes).
Drain the potatoes on paper towels and allow them to cool for 20 minutes. Increase the temperature of the deep-fryer to 375 degrees F. Deep-fry the potatoes once again in small batches, tossing occasionally, until crisp and golden brown. Drain on paper towels. Divide the potatoes into serving dishes. Pour gravy over the fries in the serving dishes and top with cheese curds. Serve immediately.