A new type of multigrain snack has been designed containing varied additions of Moldavian dragonhead (Dracocephalum moldavica L.) seeds. The antioxidant properties and the general health benefits of this plant material have already been widely acknowledged. The research discussed herein aimed to investigate the influence of the formulation and expansion method (frying) on the content of polyphenolic compounds, individual phenolic acids, and antiradical properties of innovative snacks enriched with dragonhead seeds. The highest content of polyphenols (0.685 mg GAE/mL), free phenolic acids (47.052 µg/g of dry matter), and highest radical scavenging activity (96.23% towards DPPH) were found in the fried snacks enriched with 22% of seeds. In these samples, 11 phenolic acids were detected. Strong positive correlations were seen between the addition of dragonhead and the polyphenol content (r = 0.989) and between the quantity of the enriching additive and the content of free phenolic acids (r = 0.953). The research has shown that such innovative snacks have the potential to supply health-benefiting free phenolic acids, e.g., salicylic, isoferulic, ferulic, p-coumaric, vanillic. Our studies provide an introduction to the development of a new range of functional foods.