How do I prevent shadowed areas when installing recessed lighting in a vaulted ceiling?
You need to locate the fixtures so that the cone of light lands where you want it.   The bulbs (or fixtures if it's an integrated unit) should mention the angle of the beam (for example 30 degrees), and may have a chart showing the diameter of the light at different distances.  Use this to determine your fixture locations.

In a flat-ceilinged kitchen, recessed lights would be located so the center of the beam is around the front edge of the counter and the light reaches to the back.   In your case, you'll want to make sure that the counter is lit, and the light isn't coming from behind the person at the counter, creating shadows.   You may need to get trim kits that allow the light to be angled to compensate for the angle of the ceiling.

When remodeling our kitchen, I used Google Sketchup to make a scale drawing of the kitchen layout, and checked our planned fixture layout by adding a circle showing the coverage of each fixture's pattern; this was very useful in visualizing where we might have coverage issues.

Be sure to plan for some overlap between the beams, especially in work areas, as the light is weaker toward the outside of the pattern.

Edit: In addition to your recessed lights, you may want to consider task lighting for key areas, such as a pendant or other fixture above the sink, under-cabinet lights for work areas on your counters, and possibly over any eat-in area (counter, table, etc).   In addition to extra light when you need it, they give you the option to turn the main lighting off when you're not using the area for food prep.    The downside is that you can end up with a lot of light switches.