In a large bowl combine the ground turkey, chopped herbs, cumin, garlic, onion, soaked breadcrumbs, and cheese. Mix until well blended. Form into 4 patties just a bit larger than the buns you will be serving these on. Season with salt and pepper.
Heat the olive oil in a large skillet over medium heat, add the burgers and cook until well browned on both sides, turning occasionally. These should temp out at 155-160 degrees F on an instant read thermometer. Transfer to a plate to rest. Top with a tbsp of shredded colby jack cheese.
Add the shallots to the pan that you cooked the turkey burgers in, add another tbsp of oil if needed. Add a pinch of salt to the shallots, cook over medium heat for 2-3 minutes or until softened.
Lightly butter the buns and place them in a warm skillet to brown the flat sides. Top the burgers with the shallots and avocado slices. If desired top the toasted buns with dijon mustard and arugula.