Preheat oven to 400°F. Heat oil in a medium skillet over medium heat. Add onion, carrots, celery, and garlic and cook, stirring occasionally, until softened, about 8 minutes. Scrape mixture into a very large bowl and let cool. Add the panko, eggs, mustard, ketchup, Worcestershire sauce, Tabasco, 1 ½ tablespoons of salt, and 1 teaspoon of pepper, and stir to form a paste. Using your hands, work in ground meats and cheese until combined.

Line a large roasting pan with parchment paper. Firmly pat meat mixture into 2 loaves, each about 10 inches long. Arrange loaves 3 inches apart on parchment and roast in lower third of oven for about 1 hour, until lightly browned and an instant-read thermometer inserted in center of loaves registers 150°F. Let meatloaf rest for 15 minutes, then cut into thick slices and serve with creamy onion gravy.

In a large saucepan, melt butter in olive oil. Add sliced white onions and stir to coat. Cover and cook over moderate heat until onions are very soft but not browned, 10 to 12 minutes. Stir in flour and cook for about 2 minutes. Add chicken stock and cook, whisking frequently, until gravy is thickened, 7 to 8 minutes. Stir in heavy cream and simmer onion gravy over moderate heat for about 5 minutes.

Transfer onion gravy to a blender and puree until smooth. Season with salt and black pepper. Return onion gravy to the saucepan and simmer until reduced to 5 cups, about 5 minutes.