Magnetic resonance fingerprinting (MRF) is a novel quantitative MRI (qMRI) framework that provides simultaneous estimates of multiple relaxation parameters as well as metrics of field inhomogeneity in a single acquisition. However, current bottlenecks exist in the forms of (1) scan time; (2) need for custom image reconstruction; (3) large dictionary sizes; (4) long dictionary-matching time. The aim of this study is to introduce a novel streamlined magnetic-resonance fingerprinting (sMRF) framework that is based on a single-shot echo-planar imaging (EPI) sequence to simultaneously estimate tissue T1, T2, and T2* with integrated B1+ correction. Encouraged by recent work on EPI-based MRF, we developed a method that combines spin-echo EPI with gradient-echo EPI to achieve T2 in addition to T1 and T2* quantification. To this design, we add simultaneous multi-slice (SMS) acceleration to enable full-brain coverage in a few minutes. Moreover, in the parameter-estimation step, we use deep learning to train a deep neural network (DNN) to accelerate the estimation process by orders of magnitude. Notably, due to the high image quality of the EPI scans, the training process can rely simply on Bloch-simulated data. The DNN also removes the need for storing large dictionaries. Phantom scans along with in-vivo multi-slice scans from seven healthy volunteers were acquired with resolutions of 1.1×1.1×3 mm3 and 1.7×1.7×3 mm3, and the results were validated against ground truth measurements. Excellent correspondence was found between our T1, T2, and T2* estimates and results obtained from standard approaches. In the phantom scan, a strong linear relationship (R=1-1.04, R2>0.96) was found for all parameter estimates, with a particularly high agreement for T2 estimation (R2>0.99). Similar findings are reported for the in-vivo human data for all of our parameter estimates. Incorporation of DNN results in a reduction of parameter estimation time on the order of 1000 x and a reduction in storage requirements on the order of 2500 x while achieving highly similar results as conventional dictionary matching (%differences of 7.4±0.4%, 3.6±0.3% and 6.0±0.4% error in T1, T2, and T2* estimation). Thus, sMRF has the potential to be the method of choice for future MRF studies by providing ease of implementation, fast whole-brain coverage, and ultra-fast T1/T2/T2* estimation.