Can I make white chocolate brownies based on a normal brownie recipe?

As you noticed, white chocolate doesn't have the same fat or solid makeup as regular chocolate, and in baking that will make a huge difference. The proportions of starch/binder (flour) to fat (butter & chocolate) to protein (eggs) are what make the difference between cake, brownie, fudge and everything in between.

White chocolate tends to melt faster than regular chocolate, so the baking time will be shorter, and there'll probably need to be extra flour & butter to make up the difference.

Go ahead and google for a basic recipe & then you should be able to make most of the same add-ins (nuts, extracts/flavorings) as any regular brownie recipe.

I would warn you to stay away from the "marble brownie" recipes though - they're really popular, but these are not two batters that play well with each other.

EDIT: Regular chocolate varies broadly in its fat makeup - different countries have diff regulations on what types of (natural) fats and (artificial) emulsifiers can be added to chocolate and chocolate-derived products. White chocolate has the same ingredient list as milk chocolate (w/o the cocoa solids), but again, the proportions and allowed/disallowed additives may be different. So you have to mind your brands/country-of-origin, as well as the "family" of chocolate.

Hershey's (US): http://www.thehersheycompany.com/nutrition-and-wellness/chocolate-101/types-of-chocolate.aspx

EU standards: http://europa.eu/legislation_summaries/consumers/product_labelling_and_packaging/l21122b_en.htm (If someone can find a more consumer-friendly explanation of EU chocolate labeling, that would be great.)