Melt the butter in a large stockpot over medium-high heat, add the chopped onions and salt and sauté for about 20 minutes, or until the onions are golden brown.: The moment the butter hits the pot you should hear a gentle hiss and smell a warm, nutty aroma, which signals the start of caramelization. As the onions soften they release moisture then gradually brown, transforming from translucent to rich, deep gold and finally to caramel tone; you will notice a complex sweet scent that replaces the raw sharpness of raw onions . Stir every few minutes so the pieces brown evenly and scrape the bottom to incorporate any fond, which carries concentrated sweetness. If the pot gets too hot and bits begin to burn, lower the heat immediately and add a splash of water to deglaze, because burnt fragments will make the soup bitter. One common mistake is rushing this step with high heat; that quick sear can char instead of caramelize, leaving harsh flavors rather than the desired mellow sweetness. Keeping a steady medium high and patience here is what builds the foundation of rich flavor.
Add 1 tablespoon of flour, stir to coat the onions, and sauté for another minute, until the flour becomes fragrant like pie crust.: Once the onions are deeply colored, sprinkle in the all purpose flour and toss so it coats every strand, which will give the broth slight body and help it cling to the onions . As you stir you should notice a warm, toasty aroma similar to browned pastry, and the texture will feel drier as the flour absorbs residual fat. Keeping the pan moving prevents the flour from forming lumps and ensures it cooks through; raw flour will leave a pasty flavor in the finished soup, so a brief sauté until fragrant is crucial. The surface should not burn to a dark color in this minute, if it darkens too quickly reduce the heat, because overbrowned flour introduces bitterness and masks the subtle caramel notes we worked to develop. Avoid adding too much flour , since that can thicken the broth excessively rather than giving it a gentle silkiness.
Add the beef stock, chicken stock, beef base, and thyme. Reduce the heat to low and simmer for 15 to 20 minutes.: When you pour in the beef stock and chicken stock , they should hiss softly as they meet the hot pot, and the aromas will lift as the mixture loosens the fond from the bottom, melding those browned bits into the broth for extra depth. Stir in the concentrated beef base so the soup gains an audible umami richness, then sprinkle in the thyme which releases a faint, peppery herb scent that balances the sweetness. Lowering to a gentle simmer allows the flavors to harmonize without boiling away the nuanced notes; you might see gentle rising bubbles and a sheen on the surface. Simmering for 15 to 20 minutes softens the final edge from the flour and integrates the stocks, producing a broth that tastes cohesive and robust. Watch the pot so it does not break into a rolling boil, because vigorous heat can make the broth cloudy and evaporate too much liquid. A common misstep is skimming too aggressively; you want to keep flavor while removing only obvious foam.
Serve topped with croutons and shredded Gruyère and Asiago cheese.: Assemble the bowls by ladling the hot broth over a handful of croutons , which will begin to soften as they soak, readying them for the gratin. Pile the shredded Gruyère cheese and the small accent of shredded Asiago cheese on top; the cheese should feel cool and springy when you sprinkle it, and when exposed to oven or broiler heat it melts into a bubbling, golden crust that yields a savory aroma and a satisfyingly elastic pull. If you prefer, transfer bowls briefly under a broiler until the cheese blisters and browns, watching closely because cheese can brown quickly; the crust should be bubbly and caramel flecked, not blackened. A frequent mistake is leaving the bowls under heat for too long which causes the cheese to become greasy and the croutons to disintegrate, so time this step carefully for the ideal contrast of crunchy and molten textures.