Practical experiments with solar power (in the modern sense) date back to the 19th century. In 1838, Herschel did some experiments in Cape Town, including roasting some meat; in 1870, the engineer John Ericsson drove a steam engine with a solar collector in what is now known as a "direct steam" model; at the 1878 Paris Expo Augustin Mouchot showed off the first parabolic solar collector.

From your description, it sounds like you're referring to Frank Shuman, who got started on solar in 1906. He was a major inventor in Philadelphia who patents include

Apparatus for Extracting Grease and Potash Salts From Wool

and

Process of Making Corrugated Wire Glass.

He spent the late 1900s trying to drum up support for solar power (and built, as part of this, a small toy train that ran on solar) and finally got some British investors to help him form Sun Power Company, Ltd. and build the first full solar thermal plant in Egypt (in Maadi, near Cairo) in 1912/1913 using the Nile for irrigation.

Asked to explain the principle on which sun power was operated, Mr. Shuman said that if a flat tin pan be painted dull black on the inside, then packed with cotton around the bottom and sides to prevent loss of heat, and a small quantity of water were poured in, covered with a pane of window glass, and exposed to the tropical sun, the water would soon begin to boil and give off steam.

-- New York Times, American Inventor Uses Egypt's Sun for Power, July 2, 1916

(The New York Times story above also has a picture of what one of the solar collectors at the plant looked like.)

Shuman considered his plant a success; in Scientific American, February 1914, he wrote

Sun power is now a fact and no longer in the "beautiful possibility" stage...

I'm not sure what you mean by him "greening the desert" exactly (that's a relatively modern phrase, from long after Shuman had died), but he did write about putting enough solar panels in Africa to match all coal and oil in the year 1909.

He calculated based on the Egypt plant numbers that he could save $2000 a year compared to a coal-burning plant. The startup cost for a coal plant was $3850 and for solar about $8000, so this required roughly a two year investment to break even, and then years after would result in more cost-effectiveness over coal.

If the face-off had remained just between coal vs. solar, it's possible solar would have made bigger in-roads. The problem is, oil was starting to get bigger and cheaper. While the first systematic oil drilling happened all the way back in 1859, the 1900s are when oil really started roaring in, with cheaper processes for extraction and being a denser concentration of energy than coal.

The level of technology for solar at the time also required very sunny areas, areas which at the time that were not the homes of the rich. Once they became rich, it was often due to oil.

And of course, there's World War I.

The War led to the Maadi plant being disassembled for scrap metal.

The War led to immense demand for ships; many coal ships were converted to oil at this time, which took vastly less manpower to operate.

The War caused a growing skepticism in new technology. Prior to the 1914, inventors were bringing gifts from the gods, but with the advent of war machines, new technology (which solar counted as) began to be viewed more askance.

The factors above combined to put solar on ice, so to speak, for many years after. Still, the central issue has always remained cost; cheaper alternatives kept winning out throughout the 20th century.

...

Frank, T. K. (2003). The Power of Light: The Epic Story of Man’s Quest to Harness the Sun.

Spencer, L. C. (1989). A comprehensive review of small solar-powered heat engines: Part I. A history of solar-powered devices up to 1950. Solar Energy, 43(4), 191-196.