On a flat surface, butterfly the two chicken breasts into 4 thinner pieces. Pat dry with a paper towel and season with salt and pepper on both sides.
Heat a large pan over medium-high heat. Once hot, add the oil and heat it up. Place the chicken breasts in the hot pan and cook, without moving them, for 4 minutes on the first side, then once golden and seared, flip them over and continue cooking for an additional 4 to 5 minutes until the chicken breasts’ internal temperature reaches 165F. Remove from pan onto a plate.
Make the sauce:
To the same pan, add the butter and melt it, using the back of a spatula to grease the entire surface. Add the chopped shallot and sauté, for 2 minutes, until it’s translucent and golden. Add the garlic, and stir to cook the garlic for about 30 seconds.
Add the chicken broth and milk or half and half to the pan, bringing it to a simmer while stirring the tidbits from the bottom of the pan. Add the thyme, stir to combine, reduce the heat to medium-low and simmer the sauce for 10 minutes.
Cook the asparagus:
Meanwhile, prepare the asparagus by heating up a large skillet over medium-high heat. Once hot, melt the butter. Add the garlic and sauté for 30 seconds, until fragrant.
Add the asparagus to the pan, Italian seasoning, red pepper flakes, salt, and pepper. Stir to distribute. Add the water to the pan and cover it immediately. Reduce the heat to low and simmer for 10 to 12 minutes, opening up the cover to stir occasionally.
Once the asparagus are ready, remove the lid, squeeze half a lemon over the top, stir and turn off the heat.
Combine:
Once the lemon garlic sauce is ready, add the chicken breasts back to the pan, squeeze the lemon juice into the pan, mix to combine into the sauce. Spoon some sauce over the top of the chicken and simmer for 2 minutes to heat everything through.
Serve the chicken with the cooked asparagus and lemon wedges from the remaining ½ lemon sliced into wedges.