Two-dimensional (2D) materials offer a rich platform for studying quantum phenomena, because their properties can be profoundly altered through heterostructure stacking and defect manipulation, while the resulting electronic and magnetic structure can be directly imaged via surface-sensitive probes. I will discuss several examples that highlight the remarkable potential of engineered two-dimensional (2D) materials for exploring novel quantum phases of matter driven by strong correlation and non-trivial topology using scanning tunneling microscopy (STM). I will first discuss our recent work on visualizing and manipulating 1D chiral edge states in a moiré quantum anomalous Hall (QAH) insulator of twisted monolayer-bilayer graphene (tMBLG). Here spectroscopic mapping allows us to directly identify QAH edge states, while combining electrostatic gating and tip-induced doping enables us to create and manipulate QAH edge states on-demand. I will also discuss the interplay between quantum confinement and strong correlation in engineered 1D twin-boundary defects of semiconducting 1H-MoSe₂ , which allows direct spectroscopic imaging of spin-charge fractionalization due to the formation of a 1D Tomonaga-Luttinger liquid.  I will conclude by providing a glimpse into new avenues of 2D materials engineering involving advanced atomically-precise characterization in the growing field of quantum materials.