Heat broiler to high. Wash and dry produce.

Dice potatoes into ½-inch pieces. Strip thyme leaves from stems; roughly chop leaves. Trim, peel, and halve carrot lengthwise; slice crosswise into ¼-inch-thick half-moons. Finely dice celery. Halve, peel, and finely chop onion. Peel and mince garlic.

Place potatoes in a medium pot with enough salted water to cover by 2 inches. Bring to a boil and cook until tender, 15-20 minutes.

Drain and return potatoes to pot. Mash with sour cream, 1 TBSP butter (2 TBSP for 4 servings), and 1 tsp chopped thyme until smooth and creamy, adding splashes of water as needed. Season generously with salt and pepper.

Cover to keep warm.

While potatoes cook, heat a drizzle of oil in a medium, preferably ovenproof, pan (use a large, preferably ovenproof, pan for 4 servings) over medium-high heat. Add carrot; season with salt and pepper. Cook, stirring, until slightly softened, 2-3 minutes.

Add celery, onion, and a large drizzle of oil; season with salt and pepper. Cook, stirring, until veggies are just tender, 5-7 minutes. TIP: If veggies begin to brown too quickly, add a splash of water.

Stir in garlic and 2 tsp chopped thyme; cook, stirring, until fragrant, 30 seconds.

Remove sausage* from casing if necessary; discard casing.

Add sausage to pan with veggies. Cook, breaking up meat into pieces, until browned and cooked through, 4-6 minutes.

Add tomato paste and flour; cook, stirring, until thoroughly combined, 1 minute.

Open package of chicken* and drain off any excess liquid; season all over with salt and pepper. Cook through this step as instructed, swapping in chicken (no need to break up into pieces!) for sausage.

Gradually stir ½ cup water (¾ cup for 4 servings) into pan with sausage mixture.

Stir in stock concentrate and bring to a boil. Cook until mixture is very thick, 1-2 minutes.

Taste and season with salt and pepper. TIP: If your pan isn’t ovenproof, transfer filling now to a baking dish.

Top filling with an even layer of mashed potatoes, leaving a 1-inch border around edge of pan. Evenly sprinkle mashed potatoes with cheddar. Broil until browned, 3-4 minutes. TIP: Watch carefully to avoid burning.

Let rest at least 5 minutes, then divide between plates and serve.