Erich Korngold

Wikipedia (1897-1957) [Austrian. Romantic/Modern.]
If you're just gonna listen to one: Violin Concerto, mvt 1 (Heifetz)

Background

Erich Korngold had a remarkable childhood as a child prodigy, impressing famous composers like Mahler and Strauss. He was  an accomplished, celebrated composer by age 20, and his first major compositions -- mostly operas -- had been performed to much acclaim.

The rise of anti-Semitism in Europe made performances of his pieces untenable, and he left Germany in 1934 to go to Hollywood to collaborate on a film score. He traveled back to Europe briefly, but returned to the US and stayed for twelve years. During that time, he wrote eighteen film scores, two of which earned Korngold Oscars (The Adventures of Robin Hood and Anthony Adverse).

This time spent in Hollywood ended up ruining Korngold's career as a classical composer. He was disparaged for his work in cinema, and he gave up on composing further operas. He turned, for the rest of his life, to orchestral compositions, which include a symphony, three concertos (violin, cello, and piano for left-hand only), along with chamber and other works.

Orchestral

Violin Concerto - complete (Hilary Hahn)
Sinfonietta - complete (composed when Korngold was just 15)
Cello Concerto (Quirine Viersen)

Chamber

Piano Sonata no. 1, mvt III
String Sextet

Film

Anthony Adverse (excerpts)
Sea Hawk (Overture)
The Adventures of Robin Hood Main Theme | Love Theme