Application of High-Quality Dried Olive with High Polyphenol Content for Bread Fortification: Effects on Nutritional, Technological, and Sensory Properties

New types of fortified breads have been developed from a new ingredient obtained by a two-step process for olive oil extraction, without external water addition, called high-quality dried olive (HQDO). HQDO is a minimally processed ingredient rich in phenolic compounds with beneficial health properties. HQDO has been incorporated in different percentages (1% HDQO1, 5% HDQO5, 10% HDQO10, and control CON) to study how it affects the properties of bread. The effects on the texture and shelf-life extension of the breads have also been studied. The bread samples were evaluated by a trained panel in descriptive sensorial analysis (1–10 scale). Fortified breads improve their nutraceutical quality by increasing their phenolic content from 0.19 mg GAE g−1 CON to 0.73 mg GAE g−1 at HDQO10 (using the Folin–Ciocalteu method). Antioxidant activity was increased from 1.24 mg AAE g−1 CON to 1.49 mg AAE g−1 HDQO10 (using the DPPH method). In sensory properties, all fortified breads obtained a high punctuation with a rating near to seven or superior. In “Aroma” and “Aftertaste”, the fortified breads obtained superior ratings. Finally, in “Flavour”, except for HQDO10, all of them had values close to eight. HDQO1 and HDQO5 were selected for their equilibrium between nutritional qualities and sensorial evaluation.