OK, I think I see where you're going with this, and I think I can clear it up for you. Sometimes you've got to pull on all the loose threads to untangle a knot, so let's start pulling...
The first thing to remember is that an EO never grants or creates new authority. Never. It's just an instruction to the Executive Branch on how it's supposed to do it's job in accordance with existing law.
Silver certificates had been issued by every president since Rutherford B. Hayes, so issuing them wasn't anything new. The government already had the authority to issue silver certs against the available Treasury stock of silver.
Unfortunately, you've edited out part of the EO that helps unravel it. 11110 starts with this:
"SECTION 1. Executive Order No. 10289 of September 9, 1951, as amended, is hereby further amended (a) By adding at the end of paragraph 1 thereof the following subparagraph (j):" So, EO 11110 is amending 10289--but what does 10289 do?
10289 is a list of things that the Treasury Secretary can do without getting prior presidential approval. 11110 just takes the president's already existing authority to issue silver certs, and delegates it to the Treasury Secretary. There's no new power here--just a change in who can give the order.
So, we know that the EO shifts the authority to issue silver certificates from JFK to his Treasury Secretary, C. Douglas Dillion. But why do that?
Because the same day he signed 11110, Kennedy signed PL 88-36, which did two things 1) Gave the Fed the authority to issue $1 and $2 notes (which it couldn't do before), and b) revoked the Silver Purchase Act. That's important because before PL 88-36 was signed, silver certs could be issued either by the President (under the Agricultural Adjustment Act) or by the Treasury Secretary (under the Silver Purchase Act). With the signing of PL 88-36, Secretary Dillon could no longer issue them, so EO 11110 delegated Kennedy's authority to him.
Another thing to remember is that the EO mentions silver "not then held for redemption"--IOW, new certificates could only be issued against silver that wasn't already accounted for by existing silver certs. The US had been selling its silver since the late 1950's to keep the international price down, and by the time 88-36 and 11110 were signed, there was only about $50 million in "available" silver for new certificates.
I hope that clears it up...