Heat the oven to 375ºF. Line a 9x5-inch bread pan with parchment paper, leaving a few inches of overhang on the two long sides of the pan.
Break the eggs into a large bowl. Add the olive oil and the thyme leaves. Whisk it all together until the eggs are nice and fluffy.
In another bowl, mix the almond flour, cauliflower rice, baking powder, and salt. Pour the egg mixture into the dry ingredients and thoroughly combine.
Pour the batter into the lined bread tin. Bake until a toothpick inserted in the center comes out clean, about 45–50 minutes.
Remove the bread from the oven and let it cool in the pan for 10-15 minutes.
Use the parchment paper overhang to carefully remove the bread from the pan. Transfer the bread to a wire rack to cool completely, at least 30-40 minutes. Slice and serve at room temperature.