Use a damp towel to clean off the tops of the portobello mushrooms, and then remove the stem and use a spoon to scrape out the gills.
Slice the portobellos into ½-inch wide strips.
Combine the Panko breadcrumbs, oregano, parsley and Parmesan in a small bowl. Place the flour in a second small bowl, and then lightly beat together the eggs in a third small bowl.
Bread each mushroom strip by coating it in the flour, then the eggs, and then the breadcrumbs. Set the breaded portobellos aside.
Prepare the spicy ketchup by setting a small saucepan over medium heat. Add the oil, then the garlic, and saute until golden. Add the ketchup, crushed red pepper flakes and hot sauce, stirring to combine. Cook 2 to 3 minutes until warm, then transfer to a serving bowl and set aside.
Heat 2 to 3 inches of vegetable oil in a large heavy-bottom pot over medium heat until it reaches 365ºF.
Working in small batches, fry the portobellos until golden brown, turning occasionally, for 1 to 2 minutes, or until golden brown. Transfer the portobello fries to a paper towel-lined plate and immediately season with salt. Return the oil to 365ºF between each batch and repeat frying process with remaining portobellos.
Serve the portobello fries warm with the spicy ketchup.