Cheesy Caramelized Onion Pasta with Sage Breadcrumbs

For the onions
In a Dutch oven or large, heavy-bottomed sauté pan, warm the oil and butter over medium-high heat. Add the onions and cook, stirring often, until they’re soft and golden, about 25 minutes. (If they start to scorch, deglaze the pan with a splash of water and/or turn down the heat.) Season to taste with salt.

Reduce the heat to medium. Add the vinegar and cook for 2 minutes. Add the stock and cook, stirring often, until the liquid is absorbed and the onions are deeply browned and jammy, 15 to 20 minutes. Adjust seasoning to taste and transfer to a bowl.

For the breadcrumbs
While the onions cook, warm the oil and butter in a skillet over medium-high heat. Add the breadcrumbs and a big pinch of salt and cook, stirring often, until the crumbs turn golden, about 3 to 5 minutes. Stir in the sage and turn off the heat. Transfer to a bowl.

For the rest
Start bringing a large pot of water to a boil.

In the same vessel used to cook the onions, melt the butter over medium heat. Add the flour and cook, whisking constantly, until it starts to bubble and smell nutty, about 2 minutes.

Add the milk slowly, either in a steady stream or a splash at a time, whisking continuously (at first the mixture will get very thick; it’ll thin out significantly once all of the milk is added). Increase the heat to medium-high and cook, still whisking, until the sauce starts to bubble and thicken to the consistency of a creamy soup, about 2 minutes. (You know it’s done when it coats the back of a metal spoon.)

Reduce the heat to low. Add the cheeses one handful at a time, whisking after each addition until smooth (I opted for 3 ounces of each cheese, which results in a slightly lighter sauce—do as you wish!). Season to taste with salt and plenty of freshly grated nutmeg. Stir in the reserved onions and remove from the heat.

For serving
When the water is boiling, season it generously with salt. Add the pasta, stir for a few moments to prevent sticking, and cook according to the package instructions until al dente or your liking.

Return the sauce to low heat. Using a spider sieve or slotted spoon, transfer the pasta directly to the sauce and stir to coat. (If you need to drain the pasta in a colander, reserve at least 1 cup of the cooking water before doing so.) Loosen with pasta water as needed (you will need it!) until it reaches a saucy, glossy consistency. Divide the pasta among bowls and serve, topped with the breadcrumbs.