I’m thinking that you are going to want to first create a single channel mask out of the text. White lettering on a black background. This is the “stencil” mask.
Duplicate the mask, and apply a gaussian blur to it. This becomes the “shadow” mask, and it will be larger than the stencil mask. I posted code for doing this very conveniently (and faster than the Juce blur):
Apply the stencil mask to the Graphics context as a clipping region so that drawing only takes place on the interior of the stencil.
Now, take the blurred mask and call drawImage() with fillAlphaChannelWithCurrentBrush=true after setting the current brush to some transparent level of black (or dark blue?). Draw the image at some offset from the original location.
The result will be a shadow similar to the one posted in your screenshot.