Preheat oven to 375 degrees F. In a large sauté pan over medium heat, fry the bacon, stirring occasionally, until crispy and golden, 4–6 minutes. Meanwhile, grease the baking dish with 1 tablespoon butter.
While the bacon is frying, prepare the vegetables: Cut the carrots into ¼-inch dice. Cut away and discard the dark green tops of the leeks and slice each in half. Rinse to remove sand and grit, then slice crosswise into ¼-inch slices. Set aside the carrots and leeks.
Remove thyme leaves from stem by pinching the sprig at its tip and sliding your fingers down to the other end. Set aside. Trim the end of the garlic clove, then smash with the flat of your knife to remove the peel. Mince the garlic and set aside.
When the bacon is brown and completely crisp, use slotted spoon to transfer to a paper towel-lined plate, leaving the fat in the pan. Set the bacon aside. Over medium heat, add 2 tablespoons butter to the bacon fat. Add carrots and leeks; use a wooden spatula to scrape up the browned bits, or "fond," on the bottom of the pan as you stir the vegetables. Continue to sauté until leeks are translucent, about 6 minutes. Add garlic, and sauté 1 more minute. Season to taste with salt and pepper (but remember that the cooked bacon will add more salt to the final dish).
In a large stock pot or bowl, add the toasted bread cubes, followed by the leek-carrot mixture and the cooked bacon. Gently mix to combine. Add half of the stock and all of the thyme, then use your hands to toss and combine. Add remaining stock and continue to toss. If the bread still seems dry, add more stock as needed: the cubes should be moist but not falling apart. Finish by adding the chopped green onions and giving a final toss. Transfer dressing to the prepared baking dish. Bake until crispy and golden, 45–60 minutes.
Dressing can be made 1 day in advance. Once cool, cover and refrigerate until ready to serve. Reheat in a 300 degrees F oven for 10 minutes before serving.