Melt just over half your butter in a wide, heavy-bottomed skillet or saucepan over medium heat. Swirl the pan once or twice, and as soon as the butter sighs and foams a little, add the chicken pieces. Let them sizzle, turning them every so often so they cook evenly and stay juicy—you're looking for tender bites, not browned edges.

Add the onions and carrots next, stirring so the vegetables mingle with the rendered chicken juices. Let everything soften slowly; a gentle heat brings out the natural sweetness without making the veg mushy.

Scatter in the thyme, then tumble the frozen peas and corn into the mix. Stir everything together, so the vegetables thaw and brighten up a bit.

Pull the cooked chicken and veggies to the sides of the pan. Melt in your remaining butter, then sprinkle flour straight into that buttery puddle. Stir into the pan for a minute, letting it cook off any raw taste—this is a mini roux, and it's the secret to getting that dreamy, smooth texture later on.

Slowly pour in the milk while stirring frequently (or even whisking gently if you prefer), watching the flour and butter mixture blend in and the sauce begin to thicken. Don’t rush; gentle heat keeps everything lump-free, and you’ll notice the whole mixture start to look glossy and luxurious.

Lower the heat and swirl in the heavy cream. Season to taste with salt and pepper, stopping to dip your spoon in and adjust if needed. Give it all a few minutes to simmer softly—just until the sauce coats the chicken and vegetables in one smooth, creamy blanket. You want a filling that holds together but doesn't clump.

While the filling finishes, toast your thick-cut bread until golden at the edges. Serve spoonfuls of hot, smooth filling over the top—or tuck under a pie crust or pastry lid, if you feel fancy.