Step 1

Melt the butter in a large heavy-bottomed pot or Dutch oven over medium heat. Add the onion, thyme, and 1/4 teaspoon salt, and cook, stirring occasionally, until the onion has softened and is starting to brown, about 8 minutes.

Step 2

Add the orzo and cook, stirring occasionally, until toasty smelling, about 1 minute. Add the milk, water, and remaining 3/4 teaspoon of salt, and season with pepper. Bring to a boil, then reduce the heat to medium-low and simmer, stirring occasionally, until the orzo is almost cooked through, 12 to 15 minutes. (Add more water as needed if the orzo absorbs it all before tender.) Meanwhile, prep the broccoli.

Step 3

Cut the broccoli into very small florets, about 1/2-inch pieces. When the orzo is almost ready, add the broccoli and cook, stirring occasionally, until just cooked through, about 3 minutes.

Step 4

Remove from the heat and add the tuna and cheese. Stir until the cheese is melted, then taste and add more salt as needed. Serve immediately.