Explore the spectrum of self-adjoint extensions for exceptional Laguerre-type differential expressions in this 27-minute conference talk from the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the relationship between these expressions and classical Laguerre differential expressions through Darboux transformations, expressed as explicit Weyl-Titchmarsh m-functions. Discover how boundary triples are used to parameterize self-adjoint extensions and generate Weyl-Titchmarsh m-functions. Learn about the manipulation of Maya diagrams and partitions in classifying seed functions that define relevant Darboux transforms. Gain insights into advanced topics in spectral theory and differential operators as applied to quantum theory.