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The dispersion of extragalactic fast radio bursts (FRBs) can serve as a powerful probe of the diffuse plasma between and surrounding galaxies, which contains most of the Universe's baryons. By cross-correlating the dispersion of background FRBs with the locations of foreground galaxies, we can study the relative spatial distributions of plasma and galaxies on scales of 0.1 to 50 Mpc, which are strongly affected by feedback processes in galaxy formation. Here, we present the measurement of the dispersion-galaxy angular cross-power spectrum between 2870 FRBs from the Second CHIME/FRB Catalog and nearly 6 million galaxies from the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Survey. Over five photometric galaxy redshift bins spanning <inline-formula><mml:math><mml:mn>0.05</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>z</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.5</mml:mn></mml:math></inline-formula> and at <inline-formula><mml:math><mml:mrow><mml:mn>4.9</mml:mn><mml:mi>σ</mml:mi></mml:mrow></mml:math></inline-formula> significance, we make the first definitive detection of spatial correlations in FRB dispersion measure due to cosmic structure. While parameter inferences should be interpreted with caution because of incomplete modeling of both the signal and systematic errors, our data indicate that the plasma-galaxy cross-power spectrum cuts off relative to the matter power spectrum at a scale <inline-formula><mml:math><mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>cut</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:msubsup><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.34</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.46</mml:mn></mml:mrow></mml:msubsup><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext></mml:mrow><mml:mi>Mpc</mml:mi></mml:mrow></mml:math></inline-formula>. This scale is consistent with those x-ray stacking analyses that suggest dark-matter halos with group-scale masses are largely evacuated of their baryons by feedback processes. Our Letter demonstrates that FRBs are promising tools to discern the physics of baryonic structure formation and will only become more powerful as FRB surveys expand.