Trim the corners off the bread slices so they will fit snugly into the ramekins when it's time to bake, then place all four slices in an 8x8 baking dish, or baking pan.
Whisk the cream, half-&-half, eggs, honey, and salt in a medium bowl until smooth. Pour the custard mixture evenly over the bread, flipping each slice over once to fully saturate. It's ok of there's a little left over as it will soak in over time. Cover tightly with plastic wrap and refrigerate at least 8 hours (I usually serve this at breakfast, so I soak overnight.)
When ready to bake, crank the oven to 375 F. Divide 1 tablespoon of the butter equally among the 4 ramekins and thoroughly coat the interiors (fingers are best for this), and place them on a half sheet pan or a cookie sheet with a lip.
Combine the remaining 4 tablespoons butter, brown sugar, rum, and vanilla extract in a small saucepan and cook for 3 minutes, over medium heat, whisking frequently. Kill the heat and whisk in the rosemary. Immediately pour the hot sugar glaze equally into the ramekins, followed by equal portions of the pecans.
Using an angled spatula or fish turner, carefully transfer the soaked bread to the ramekins. Place them on the middle rack of the oven and bake for 25 minutes, until the glaze is bubbling, and the tops are lightly golden. Remove from the oven to a cooling rack and rest 5 minutes. Have 4 small serving plates standing by.
Loosen the edges of the toasts with a small knife or metal spatula. Place a small plate on top of the ramekin and cover with a dry kitchen towel. Carefully flip, inverting the French toast on to the plate, so the nuts are on top, and the glaze oozes over the edges.
Serve immediately and be prepared for all who taste it to swear their undying love.