Let's get into the technicalities of FROM WHERE the authority of an "EXECUTIVE ORDER BY THE PRESIDENT".
To quote your clarification, you wrote
"They" [the President, and the Executive branch] "can make ANY regulation they want."
That is
NOT TRUE.
Let's go to the part that IMPLIES the President can issue what we call "Executive Orders" located in
ARTICLE II, SECTION 3, of the United States Constitution :
He shall from time to time give to the Congress Information of the State of the Union,
and recommend to their Consideration such Measures as he shall judge necessary and expedient;
he may, on extraordinary Occasions, convene both Houses, or either of them,
and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper;
he shall receive Ambassadors and other public Ministers;
he shall take Care that the Laws be faithfully executed,
and shall Commission all the Officers of the United States.
Here is what
"the Congressional Research Service" states on page 1 of their report :
" ... Presidents have historically utilized various written instruments to direct the executive branch and implement policy.2
These include executive orders, presidential memoranda, and presidential proclamations.
The definitions of these instruments, including the differences between them, are not easily discernible, as the U.S. Constitution does not contain any provision referring to these terms or the manner in which the President may communicate directives to the executive branch. ... "
Now that being PROVEN, let's get back to the erroneous statement you wrote
"They" [the President, and the Executive branch] "can make ANY regulation they want."
Executive Orders HAVE LIMITS and that has been proven also.
"The Congressional Research Service" states in their introduction that :
The President’s authority to issue executive orders does not include a grant of power to implement policy decisions that are not otherwise authorized by law.
Indeed, an executive order that implements a policy in direct contradiction to the law will be without legal effect unless the order can be justified as an exercise of the President’s exclusive and independent constitutional authority.1
So to summarize that:
Any executive order MUST IDENTIFY whether the order is based on the powers given to the president BY the U.S. Constitution
or delegated to him BY Congress.
And :
Executive orders are subject to legal review,
and the Supreme Court or lower federal courts can nullify, or cancel, an executive order if they determine it is unconstitutional.
Similarly, Congress can revoke an executive order by passing new legislation.