Fudgy brownies have a higher fat-to-flour ratio than cakey ones. So add more fat -- in this case, butter and chocolate. A cakey batch has more flour and relies on baking powder for leavening. The amount of sugar and eggs does not change whether you're going fudgy or cakey.
See the recipes below to get an idea of the ratios needed to achieve your ideal brownie.
Thomas's Cakey Brownies
A little less chocolate, a little less butter, but more flour yields a taller, more cakey brownie -- that bakes faster than its fudgy relation.
Thomas's Fudgy Brownies
If your batch is still not fudgy enough, gradually increase the amount of butter and chocolate, or decrease the flour.
Now, watch Thomas Joseph explain the science behind the perfect brownie: