The current trend is represented by replacing solid fats with structured liquid oil while maintaining the plastic properties of food products. In this study, the behavior of refined sunflower oil structured with various agents (carnauba wax-CRW, β-sitosterol:beeswax-BS:BW, β-sitosterol:lecithin-BS:LEC, and glycerol monostearate-GM) was evaluated in the process dynamics of oleogel-based tender dough products. The oleogel with the mixture of β-sitosterol:beeswax (OG_BS:BW) displayed the highest capacity to retain oil inside the matrix with a percentage of oil loss as low as 0.05% and also had a significantly higher hardness (6.37 N) than the reference, a commercial margarine (MR—3.58 N). During cooling from 90 to 4 °C, the increase in oleogel’ viscosity results from oleogelator’s liquid–solid phase transition. As demonstrated by the frequency sweeps performed, storage modulus G′ was higher than loss modulus G″, no cross-over points were observed, and the strongest gel network was for the oleogel with glycerol monostearate (OG_GM). Regarding the dough, the sample prepared using the oleogel with carnauba wax (D_CRW) showed the strongest hardness (92.49 N) compared to the reference (D_MR—21.80 N). All the oleogel-containing doughs had elastic solid-like behavior. The samples with margarine (D_MR) and the mixture of β-sitosterol:lecithin (D_BS:LEC) presented the lowest value of both moduli of G’ and G” during the frequency sweep. The biscuits formulated with commercial margarine (B_MR) registered a hardness of 28.74 N. Samples with oleogels showed a specific tenderness for tender dough products, thus being suitable for this type of product (11.22–20.97 N).