Heat the oven to 425 °F and line a baking sheet with parchment paper. The hot oven helps the phyllo crisp quickly, and the parchment keeps the bottoms from sticking.
Stir the feta, dill, and grated garlic together in a bowl, then pour about 1/4 cup olive oil into a separate bowl for brushing. The filling should look evenly mixed, and having the oil ready makes assembly much easier.
Lay one phyllo sheet on a clean work surface and fold it in half crosswise. Don’t worry if a sheet tears a little, because the layers usually cover small imperfections.
Brush a little olive oil around the edges, place 1 rounded tablespoon of feta filling on the short end, then roll it up tightly while folding in the sides like a burrito. A snug roll with tucked sides helps keep the filling in place during baking.
Set the roll seam-side down on the prepared sheet and repeat with the remaining phyllo and filling to make 12 to 16 rolls. Keeping the seam underneath helps the rolls stay closed instead of unraveling in the oven.
Brush the tops with olive oil and bake for 20 min. The rolls are ready when they are deep golden brown, crisp on top, and lightly hollow-sounding when tapped.
While the rolls bake, melt the butter with 1 tablespoon oil, the chili flakes, and cumin in a small skillet over medium heat. Cook just until the spices smell fragrant, about 1 to 2 min, which blooms their flavor without burning them.
Take the skillet off the heat and stir in the honey until smooth. The sauce should look glossy and pourable, with a warm sweet-spicy aroma.
Serve the rolls warm with the chili honey for dipping or drizzling. The contrast is best when the pastry is still crisp and the sauce is slightly warm.