Vine Hill Capital Investment Corp. Unit (VCIC) S-1/A IPO registration (amended)

Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the use in the Prospectus constituting a part of this Registration Statement on Amendment No. 2 to Form S-1 of our report dated August 16, 2024, relating to the financial statements of Vine Hill Capital Investment Corp. as of May 28, 2024, and for the period from May 24, 2024 (inception) through May 28, 2024, which is contained in that Prospectus. We also consent to the reference to our firm under the caption “Experts” in the Prospectus.

/s/ WithumSmith+Brown, PC

New York, New York

August 16, 2024