Step 1 Grill the onions: Heat a grill or grill pan over medium-high heat until hot. Lightly brush the green onions with oil, then grill, turning every minute or so, until charred on all sides. Remove from heat and set aside until cool, then slice crosswise into small rings.
Step 2 In the bowl of a stand mixer fitted with the whisk attachment, or in a large bowl using a hand mixer, beat together the egg yolk, salt, mustard, sugar, lemon juice, cane vinegar and Worcestershire sauce until incorporated. With the mixer running, slowly add the oils until you reach a mayonnaise-like consistency. Fold in the green onions and sweet pickle relish. Cover and refrigerate until ready to use. This makes about 1 cup tartar sauce, which will keep, covered and refrigerated, up to 5 days.