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Cut the chicken breasts in half lengthwise so you've got 4 thinner pieces. Sprinkle them with salt (some lemon pepper blends contain salt so don't go overboard).
Add the oil and 1 tablespoon of the butter to a skillet over medium-high heat. Let the pan heat up for a few minutes.
Sear the chicken for 4-5 minutes/side, then transfer it to a plate.
Add the remaining butter to the pan and let it melt, then add in the garlic and sprinkle the flour in. Let it cook for about 30 seconds to 1 minute (stir it a couple times).
Add the broth, cream, and lemon pepper to the skillet. Whisk it for a minute or so until the flour dissolves.
Add the chicken back to the pan (and any juices from the plate), and let it cook for another 4-5 minutes or until the chicken has cooked through (165F) and the sauce has thickened a bit. You may need to turn the heat down if it's boiling like crazy (you want it to bubble fairly gently). Season with extra salt & pepper if needed and serve immediately.