Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 2$ cm. What is the area of the shaded region?

[asy]
import graph;
fill(Circle((0,0),20),gray(0.7));
draw(Circle((0,0),20));
draw((-16,12)--(16,-12)--(0,-20)--cycle);
fill((-16,12)--(16,-12)--(0,-20)--cycle,white);
label("$A$",(-16,12),NW);
label("$B$",(16,-12),SE);
label("$C$",(0,-20),S);
label("$P$",(0,0),N);
dot((-16,12));
dot((16,-12));
dot((0,0));
dot((0,-20));
[/asy]
The area of the shaded region equals the area of the circle minus the area of the triangle.  The area of the circle is $2^2\pi=4\pi$.  To find the area of the triangle, we look for information about the triangle.  Because angle $ACB$ intersects $180^\circ$ of the circle, we know $m\angle ACB=\frac{180^\circ}2=90^\circ$, so triangle $ACB$ is a right triangle.  What's more, since $AB=4$ and $BC=2$, it follows that $AC=2\sqrt{3}$ and the area of right triangle $ACB$ equals $\frac{2\cdot2\sqrt{3}}2=2\sqrt{3}$.  So, the area of the shaded region is $\boxed{4\pi - 2\sqrt{3}}$.