An executive order is a way of memorializing in writing Presidential authority that is either expressly granted to the President by the constitution or statute, or is left to President by implication either from a lack of guidance or as a result of the structure of the constitution and historical precedent.
Congress has wide discretion to legislate in a manner that limits the power to make executive orders and pass regulations, and can mandate that the administration issue regulations in a certain area or refrain from issuing regulations in a certain area where the Executive branch is denied discretion or denied the right to set overarching policies as opposed to deciding things on a case by case basis at a lower level in the bureaucracy.
In principle, Congress could so micromanage the executive branch that it would be unconstitutional, but that is basically a hypothetical concept with no meaningfully well defined boundaries. The hard cases involve grants of regulatory authority subject to further approval by a subpart of Congress like a committee, as opposed to a full fledged act of law (something called a "legislative veto") which has dubious constitutional status despite being common.
The main "meta-legislation" governing regulations in general in the federal government is the Administrative Procedures Act.
Subject to the limitations imposed by Congress, a President can take any approach desired to making and changing regulations, but the APA does impose meaningful limits, in particular, on how and how fast, existing regulations can be changed, which may make it hard to eliminate two regulations for each new one that the administration wants to pass or is mandated by Congress to adopt to implement statutes it has passed.
But, because a "regulation" is not a meaningfully defined unit, it is a pretty meaningless edict. You can satisfy it simply by cramming two sections of a bunch of regulations into one, essentially reformatting it for political cosmetics rather than making substantive changes, or by incorporating something else by reference. So, the 2 for 1 EO is basically an aspirational statement of policy and attitude more than it is a meaningful constraint. No one could sue the administration or invalidate a regulation it passed because it didn't comply with this EO.