In a large, wide skillet (large enough to fit the ham) over medium-high heat, cook the ham until tender and lightly browned (typically 2-4 minutes per side, until desired doneness). Set ham aside on a covered plate to keep warm.
Reduce heat to medium, then add butter; allow to melt. Sprinkle in flour and cook, whisking constantly, until mixture turns the color of peanut butter, about 5 minutes.
Slowly pour a small amount of bone broth in the skillet, continuing to whisk constantly. Once the bone broth has been absorbed, pour in a little more and again whisk until absorbed. Repeat this step until all bone broth has been added.
Continuing to whisk, slowly pour in coffee until gravy is smooth.
Season gravy with sugar and salt, then whisk well.
Allow gravy to cook, whisking occasionally, until it begins to thicken and bubbles start to form. Remove gravy from heat.
Serve red eye gravy immediately, drizzled on top of the cooked country ham steak.
Recipe should make slightly more than 1 cup red eye gravy (depending on thickness).
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