First I made a new layer, the plan was to have two layers as I needed two paths for some of the letters. This meant that I could export it to Photoshop as two layers also. We will create all of the first layer (red) then afterwards create the second (green). Hit P to select the pen tool, the pen tool in Illustrator works in the same way as in Photoshop. We don't want any bezier curves so click once at each point and don't drag the mouse. Draw this shape in your document; starting from the lower left point. We have to start at the right end or else the colors wont match up when we add layer 2.
Hit V then click on the path and a bounding box should appear. In the main toolbar make sure we have no stroke or fill then just click on our brush in the brushes panel and it should look like the image below. If for example our brush was the wrong size we could click the small button to the left of new brush and change the size but since we set it at 20% already we should be fine.
Now for quick bit of maths; go edit>preferences>guides & grid and take note of the 'gridline every:' number, now divide this number by 4, mine was at 72px so I got 18. This number is because we are going to round the corners and want the radius to be equal to two of the minor gridlines; the reason for this is obvious if you look at the examples of the letters I used but if you were to use different letters you could make it more or less rounded. Okay to round the corners, with the leter still selected, go effect>stylize (illustrator)>round corners and set it to the value you calculated.
Do the same for the other letters, so all my paths looked like the image below. You can either do the letters one at a time or create all the paths then add the styles to all of them at the same time. The image below that shows the completed first layer of the letters.
Now for the second layer, do exactly the same as for the first, In green is the paths I used for the second layer, I then added the same styling to achieve a result like the one below. Note that here you could always just copy the R to save creating it again. You should have three layers; one with the brush shape in it, another with the first layer of our text (red) which we'll call T1 and another with our second layer of text (green) which we'll call T2.
Create a new document in Photoshop; since these are vectors you can make it any size but I used 900x300px as I envisioned it as a good idea for a website header. Now in Illustrator, hide T2 then drag a selection on over the text then copy and paste it into Photoshop as a smart object if possible, if not then paste it as pixels and ignore the next bit. Hit Ctrl+T then change the height and width to 150%. Now do exactly the same with T1, hiding the T1 in Illustrator, then alaign it with the other layer. Below I've only shown one letter but that's only because I'll be demonstrating the techniques on this letter first.
Ctrl+click on T1 to make a selection around it. There is a few steps that aren't required for the text I used but you may need to do all steps If you are doing this to a different shape or size of text so I'll show you all the steps then you can work out the shortcuts if you want. Select the polygonal lasso tool then hold Shift to change it to add mode, this will add to the selection we already have. Now draw around the parts of T2 that you want to hide (purple line), one letter at a time. So here I've made this selection which will keep the same curve at the right part of the R by staying within this line then drawing round everything else. The resulting selection is shown below that.