A new cultivar of Lavandula x intermedia plant named ‘;Tesseract’; that is characterized by its foliage that is very broad and bright silver with a very thick substance, its very compact and strongly upright plant habit, its flowering stems that are strong and held upright and straight making it ideal for fresh or dry cut flowers, its large flowers on very densely flowered flower spikes, its flower petals that are a bright and deeply saturated purple color, its flower stems that are very thick and branched resulting in rebloom for a longer blooming season, its tolerance to leaf spotting and root disease, and its strong, pleasant lavender fragrance.