Yes, there is!

The best place I know where this is done are the initial sections of

J. J. Duistermaat, J. A. C. Kolk, and V. S. Varadarajan. Functions, ﬂows and oscillatory
integrals on ﬂag manifolds and conjugacy classes in real semisimple Lie groups. Compositio
Math., 49(3):309–398, 1983

I don't know much about complex groups (I work in the real context), but the above article also considers the complex case. Below I give you a picture of what happens for a real Lie semisimple noncompact Lie group $G$, hope this can help.

The key is the action of a regular split-element of the Lie algebra on the maximal flag manifold $\mathbb{F} = G/P$ of $G$: this action is Morse, and the Morse function is beautifully simple: it is the height function of a natural embeeding of $\mathbb{F}$ in the Lie algebra of $G$ under an appropriate metric on $\mathbb{F}$. Its critical points are computed to be $wP$ and their stable manifolds are computed to be $PwP$.

In case you are interested, they even prove the double-coset Bruhat decomposition
$$G = \coprod_w P_\Theta w P_\Delta,$$
which is disjoint when $w$ runs trough the double coset $ P_\Theta \backslash W / P_\Delta $. Here $P_\Theta, P_\Delta$ are the standart parabolic subgroups of type $\Theta$ and $\Delta$: they contain the minimal parabolic subgroup, which plays the role of the Borel subgroup in the real theory. The key here is the action of a (possibly not regular) split-elemet on $\mathbb{F}$: this action is Morse-Bott with the same beatifull Morse function! Its critical manifolds are computed to be the orbits of $wP_\Delta$ and their stable manifolds are computed to be the orbits of $P_\Theta w P_\Delta$ on the flag manifold. The hard part is to show that the above critical manifolds are indeed disjoint: to do this the above article appeals to algebraic constructions involving Tits buildings and other things I don't understand... This was disappointing to me since I expected a self-contained purely dynamical solution!

After some stubborn tries I was able to do this step by purely dynamical arguments. It turns out that these critical manifolds are again flag manifolds: actually, flag manifolds of semisimple subgroups of $G$! This came as a nice surprise to me and my PhD advisor. Using this fact and the previous regular Bruhat decomposition, one can show by some simple dynamical arguments that these critical manifolds are disjoint. So the question can be settled by purely dynamical arguments and in a nice inductive manner. This is the content of my article

Seco, L. . "A Note on the Bruhat Decomposition of Semisimple Lie Groups". Journal of Lie Theory, v. 18, p. 725-731, 2008.

I would be very interested to know if the same method applies in the complex case to obtain an analogous double-coset Bruhat decomposition.