Preheat the oven to 400 degrees F. Heat the olive oil in a large cast iron-skillet over medium high heat. Add the potatoes, carrots, onion and butternut squash and let cook until golden brown, about 5 minutes. Add the thyme springs, butter and some salt and pepper and let the butter melt.
Sprinkle the flour over the vegetables, stir to combine and cook for 3 minutes. Slowly stir in the chicken broth and milk and cook until thickened. Stir in the Cheddar.
Top the vegetables with the breadcrumbs bake until golden brown and bubbly, 15 to 20 minutes. Let rest for 10 minutes before serving.