That's actually fairly easy to achieve. Here are the 2 things you should do:
1 - lower the gamma in the tweaks tab of the cloud layer to below 0.3 (to begin with)
2 - increase the density in the cloud fractal until your sky is covered again
what this does in simple terms is that the reduced gamma brings out the vertical features of the clouds more. This is really very much simplified but you can look at it this way. The side effect is that less features from the cloud fractal qualify for being rendered, and only a fraction of the fractal features are above pure white (below a certain level of grey the cloud won't show / render, and above a certain level of white the have the max height, which can look like a flat white area when seen from above). So to make up for it, you have to increase the coverage a lot.
Frank