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In a previous work we have introduced and studied the notion of embedded$\mathbf{Q}$-resolution, which essentially consists in allowing the finalambient space to contain abelian quotient singularities. Here we explicitlycompute an embedded $\mathbf{Q}$-resolution of a Yomdin-L\^e surfacesingularity $(V,0)$ in terms of a (global) embedded $\mathbf{Q}$-resolution oftheir tangent cone by means of just weighted blow-ups at points. Thegeneralized A'Campo's formula in this setting is applied so as to compute thecharacteristic polynomial. As a consequence, an exceptional divisor in theresolution of $(V,0)$, apart from the first one which might be special,contributes to its complex monodromy if and only if so does the correspondingdivisor in the tangent cone. Thus the resolution obtained is optimal in thesense that the weights can be chosen so that every exceptional divisor in the$\mathbf{Q}$-resolution of $(V,0)$, except perhaps the first one, contributesto its monodromy.

Embedded $\mathbf{Q}$-Resolutions for Yomdin-L\^{e} Surface Singularities