Offer Letter Says “at-will Employment” But Also Mentions Notice Period

Location: Texas, USA
I signed an offer letter around a year ago when I started working for my current employer. It states this:
“At-Will Employment: You understand that your employment with the Company is at-will and may be terminated by you or the Company at any time, with or without cause and without notice. However, the Company shall have the right in either case, to invoke a 30-day notice period, which shall be used for transitioning of your responsibilities to a successor. Nothing in this agreement is intended to constitute an agreement for employment for a specific period of time. Notwithstanding the foregoing, you acknowledge that certain egregious conduct in connection with your employment may justify immediate termination of your employment with the Company.”
There is no mention anywhere of any penalties for not giving 30 days notice. I am planning to switch jobs and give 2 weeks notice. Can I legally do so? What repercussions might I deal with if I only give 2 weeks notice?
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