1. Start by slicing your streaky bacon into 1cm lardons. Heat a large pan over medium heat and cook the bacon until crispy, about 5-7 minutes. Remove the cooked bacon with a slotted spoon, setting it aside on kitchen paper, and leave the rendered fat in the pan.

2. Pat the pigeon breasts dry and season with salt and pepper. Return the pan (with bacon fat) to medium-high heat. Add a drizzle of olive oil if needed. Once hot, place the pigeon breasts in the pan. Sear the pigeon breasts in batches if necessary to avoid overcrowding the pan, which would steam them instead of searing. Cook for 2-3 minutes per side until nicely browned, then flip. Add butter and thyme/rosemary. Baste the breasts for another 2-3 minutes for medium-rare. Remove the pigeon and let it rest for 5 minutes before slicing.

3. While the pigeon rests, add wild mushrooms to the same pan and sauté over medium-high heat for 3-5 minutes until golden. Stir in minced garlic and shallot, cooking for 1-2 minutes until fragrant and softened. Season with salt and pepper. Stir in white wine vinegar and cook for another minute until it's slightly evaporated. Remove the mixture from the pan.

4. Toast your sourdough bread slices until golden.

5. To assemble, slice the rested pigeon breasts. Place one toasted sourdough slice on each plate. Divide the mushroom mixture evenly over the sourdough. Arrange two sliced pigeon breasts on top of the mushrooms for each sandwich. Finish by scattering the crispy bacon lardons over both sandwiches. Serve immediately.