Amino acid-based poly(ester urea)s are an attractive class of polymers that are of interest for a variety of biomedical applications. Generally, amino acid-based poly(ester urea)s are prepared by polymerization of diamines, which are obtained from the corresponding amino acids and aliphatic diols. This article presents an alternative synthetic strategy that uses diamine monomers obtained from aromatic, 4-hydroxycinnamic acid-derived diols. A library of structurally related diamine monomers has been prepared by coupling l-leucine to 4-hydroxycinnamic acid-based diols that incorporate alkyl spacers of different lengths. The exploration of 4-hydroxycinnamic acid as a building block is interesting as it can be obtained from various biological resources, such as for example lignin, and thus provides an opportunity to take advantage of (under-utilized) bio-based renewables for the design of new polymer materials. These diamine monomers can be copolymerized in a solvent-free, one-pot, two-step process using dimethyl carbonate as an environmentally sustainable reagent to afford amino acid-based aromatic poly(ester urea) homo- and copolymers with thermal properties that can be tuned by varying the chemical structure of the diamine monomer, or via copolymerization of two different monomers.